HCF of 8 and 12 | How to Find HCF of 8 and 12 The HCF of 8 and 12 is 4. The Highest Common Factor of two or more numbers is defined as the largest positive integer that divides the numbers without leaving a remainder. In the given set of numbers 8 and 12, 4 is the Greatest Common Factor (GCF) that divides both 8 and 12.

Contents

- 1 What is the GCF and LCM of 8 and 12?
- 2 What is the GCF of 12?
- 3 Is the GCF of 8 and 12 24?
- 4 What are the multiples of 8 and 12?
- 5 What is GCF and LCM?
- 6 What are the first three common multiples of 8 and 12?
- 7 Do you multiply GCF?
- 8 Can GCF ever be 1?
- 9 Is 24 the LCM of 8 and 12?
- 10 Is 24 a factor of 8 and 12?
- 11 What is the GCF of 8 and 10?
- 12 What is the LCM GCF of 8 10 and 12?
- 13 Is the GCF of 8 12 and 16?

## What is the GCF and LCM of 8 and 12?

GCF of 8 and 12 by Listing Common Factors –

Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12

There are 3 common factors of 8 and 12, that are 1, 2, and 4. Therefore, the greatest common factor of 8 and 12 is 4.

### What is the LCM of 8 and 12?

What is LCM of 8 and 12 – The Least Common Multiple or Lowest Common Multiple of 8 and 12 is 24.

## What is the GCF of 12?

The factors of 12 include: 1, 2, 3, 4, 6, and 12. Thus, the common factors of 16 and 12 are: 1, 2, and 4. Often in math problems, it can be desirable to find the greatest common factor of some given numbers. In this case, the greatest common factor is 4.

#### What is the prime factorization of 12 and 8?

HCF of 8 and 12 by Prime Factorization – Prime factorization of 8 and 12 is (2 × 2 × 2) and (2 × 2 × 3) respectively. As visible, 8 and 12 have common prime factors. Hence, the HCF of 8 and 12 is 2 × 2 = 4. ☛ Also Check:

- HCF of 24 and 32 = 8
- HCF of 52 and 117 = 13
- HCF of 324 and 144 = 36
- HCF of 60 and 72 = 12
- HCF of 120 and 150 = 30
- HCF of 40 and 80 = 40
- HCF of 17 and 19 = 1

- Example 1: Find the highest number that divides 8 and 12 exactly. Solution: The highest number that divides 8 and 12 exactly is their highest common factor, i.e. HCF of 8 and 12. ⇒ Factors of 8 and 12:
- Factors of 8 = 1, 2, 4, 8
- Factors of 12 = 1, 2, 3, 4, 6, 12

Therefore, the HCF of 8 and 12 is 4.

- Example 2: Find the HCF of 8 and 12, if their LCM is 24. Solution: ∵ LCM × HCF = 8 × 12 ⇒ HCF(8, 12) = (8 × 12)/24 = 4 Therefore, the highest common factor of 8 and 12 is 4.
- Example 3: For two numbers, HCF = 4 and LCM = 24. If one number is 8, find the other number. Solution: Given: HCF (y, 8) = 4 and LCM (y, 8) = 24 ∵ HCF × LCM = 8 × (y) ⇒ y = (HCF × LCM)/8 ⇒ y = (4 × 24)/8 ⇒ y = 12 Therefore, the other number is 12.

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## Is the GCF of 8 and 12 24?

Answer and Explanation: The greatest common factor of 8, 12, and 24 is 4.

## What are the multiples of 8 and 12?

Common multiple of 8 and 12 are 24 and every subsequent multiple of 24. So 24 is a common multiple of 8 and 12 this means the other common multiples of 8 and 12 are the multiples of 24 like 48,72,96 etc.

### What is the GCF of 8 and 12 and 16?

Answer and Explanation: The greatest common factor 16, 8, 12 is 4.

#### What is a GCF in math?

About Transcript. The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

## What is GCF and LCM?

Review – Let’s wrap up with a couple of true or false review questions: 1. The least common multiple of 45 and 60 is 15. The answer is false. The greatest common factor of 45 and 60 is 15, but the least common multiple is 180.2. The least common multiple is a number greater than or equal to the numbers being considered.

The answer is true. The least common multiple is greater than or equal to the numbers being considered, while the greatest common factor is equal to or less than the numbers being considered. Thanks for watching, and happy studying! There are a variety of techniques for finding the LCM and GCF. The two most common strategies involve making a list, or using the prime factorization.

For example, the LCM of 5 and 6 can be found by simply listing the multiples of \(5\) and \(6\), and then identifying the lowest multiple shared by both numbers.\(5, 10, 15, 20, 25, \mathbf, 35\) \(6, 12, 18, 24, \mathbf, 36\) \(\mathbf \) is the LCM.

- Similarly, the GCF can be found by listing the factors of each number, and then identifying the greatest factor that is shared.
- For example, the GCF of \(40\) and \(32\) can be found by listing the factors of each number.
- 40\): \(1, 2, 4, 5, \mathbf8, 10, 20, 40\) \(32\): \(1, 2, 4, \mathbf8, 16, 32\) \(\mathbf8\) is the GCF.

For larger numbers, it will not be realistic to make a list of factors or multiples to identify the GCF or LCM. For large numbers, it is most efficient to use the prime factorization technique. For example, when finding the LCM, start by finding the prime factorization of each number (this can be done by creating a factor tree). Now multiply all of the factors (remember not to double-count those circled \(2\)s). This becomes \(2\times2\times5\times2\times2\times2\), which equals \(160\). The LCM of \(20\) and \(32\) is \(160\). When finding the GCF, start by listing the prime factorization of each number (this can be done by creating a factor tree).

- For example, the prime factorization of \(45\) is \(5\times3\times3\), and the prime factorization of \(120\) is \(5\times3\times2\times2\times2\).
- Now simply multiply all of the factors that are shared by both numbers.
- In this case, we would multiply \(5\times3\) which equals \(15\).
- The GCF of \(45\) and \(120\) is \(15\).

The prime factorization approach can seem like a fairly lengthy process, but when working with large numbers it is guaranteed to be a time-saver. There are two main strategies for finding the GCF: Listing the factors, or using the prime factorization.

The first strategy involves simply listing the factors of each number, and then looking for the greatest factor that is shared by both numbers. For example, if we are looking for the GCF of \(36\) and \(45\), we can list the factors of both numbers and identify the largest number in common. \(36\): \(1,2,3,4,6,\mathbf9,12,18,36\) \(45\): \(1,3,5,\mathbf9,15,45\) The GCF of \(36\) and \(45\) is \(\mathbf9\).

Listing the factors of each number and then identifying the largest factor in common works well for small numbers. However, when finding the GCF of very large numbers it is more efficient to use the prime factorization approach. For example, when finding the GCF of \(180\) and \(162\), we start by listing the prime factorization of each number (this can be done by creating a factor tree).

- The prime factorization of \(180\) is \(2\times2\times3\times3\times5\), and the prime factorization of \(162\) is \(2\times3\times3\times3\times3\).
- Now look for the factors that are shared by both numbers.
- In this case, both numbers share one \(2\), and two \(3\)s, or \(2\times3\times3\).
- The result of \(2\times3\times3\) is \(18\), which is the GCF! This strategy is often more efficient when finding the GCF of really large numbers.

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of \(24\) and \(36\) is \(12\), because the largest factor that is shared by \(24\) and \(36\) is \(12\).

- 24\) and \(36\) have other factors in common, but \(12\) is the largest.
- There are a variety of techniques for finding the lowest common multiple.
- Two common approaches are listing the multiples, and using the prime factorization.
- Listing the multiples is just as it sounds, simply list the multiples of each number, and then look for the lowest multiple shared by both numbers.

For example, when finding the lowest common multiple of \(3\) and \(4\), list the multiples: \(3\): \(3,6,9,\mathbf,15,18\) \(4\): \(4,8,\mathbf,16,20\) \(\mathbf \) is the lowest multiple shared by \(3\) and \(4\). Listing the multiples is a great strategy when the numbers are fairly small. Now multiply all of the factors (remember to only count the \(2\)s once). This becomes \(2\times19\times3\times7\), which equals \(798\). The LCM of \(38\) and \(42\) is \(798\). Taking out the LCM is a helpful skill when adding or subtracting fractions. Question #1: What is the greatest common factor of 16 and 42? Use it to reduce the fraction \(\frac \). GCF is 8, and we reduce to \(\frac \). GCF is 1, and we cannot reduce any further. GCF is 4, and we reduce to \(\frac \). GCF is 2, and we reduce to \(\frac \). Show Answer Answer:

- The correct answer is D: GCF is 2, and we reduce to \(\frac \).
- Let’s approach this problem by listing the prime factors of both the numerator and the denominator. \(16=2×2×2×2\)
- \(42=2×3×7\)
- Here we see that 2 is the only shared factor of 16 and 42 and is therefore their greatest common factor. We can then divide both numbers by 2 to reduce the fraction: \(\frac =\frac \)

Hide Answer Question #2: Find the least common multiple of 2, 6, and 8. Show Answer Answer:

- The correct answer is C: 24.
- For this problem, let’s list the prime factors of each number. \(2=2\) (note that we could write \(2\times1\), but 1 is understood, or implied, and usually not necessary to write) \(6=2\times3\)
- \(8=2\times2\times2\)

Remember, when calculating the LCM of two or more numbers, we list each prime factor once that is shared by all of the numbers. Since each of our numbers has 2 as a prime factor, our LCM will also have 2 as one of its prime factors. LCM \(=2\times\) _ Now from the 6 we have a leftover 3, and from the 8 we have two 2’s remaining.

We multiply those in to get LCM \(=2\times3\times2\times2=24\) Notice that even though 2, 6, and 8 are all factors of 48, the solution is not D, because 48 is not the smallest common multiple. Hide Answer Question #3: List the first several multiples of 3, 5, and 6 to find the least common multiple. Show Answer Answer: The correct answer is B: LCM is 30.

The first several multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, The first several multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, The first several multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, As we see above, 30 is the first (least) number that 3, 5, and 6 have in common among their multiples, so the least common multiple is 30.

- The correct answer is D: 5 bags, with 18 pieces of candy in each.
- To begin, list the prime factors of both 54 and 36: \(54=2\times3\times3\times3\)
- \(36=2\times2\times3\times3\)

Notice that they both share a 2 and two 3’s. The product of these shared prime factors is \(2\times3\times3=18\). We now know that the GCF is 18, which means each bag will contain 18 pieces of candy. Courtney’s 54 pieces will make 3 bags, and Trish’s 36 pieces will make 2 bags.

- The correct answer is C: 12 apples and 12 bananas.
- With this problem, we want to know the least common multiple of 4 and 6. Using the prime factors method, we see that \(4=2\times2\) \(6=2\times3\)
- LCM \(=2\times2\times3=12\)
- Sara will buy three bags of apples and two bunches of bananas in order to have 12 of each fruit.

Hide Answer 838699 249197 520269 946579 by | This Page Last Updated: February 17, 2023 : What is the Greatest Common Factor and Least Common Multiple?

#### What are the first 8 factors of 12?

What are the Factors of 12? – The factors of 12 are the numbers that divide 12 exactly without leaving any remainder. As 12 is an even, it has many factors other than 1 and 12. The factors of 12 can be positive or negative. Hence, the factors of 12 are 1, 2, 3, 4, 6 and 12. Similarly, the negative factors of 12 are -1, -2, -3, -4, -6 and -12.

Factors of 12: 1, 2, 3, 4, 6 and 12. Prime Factorization of 12: 2×2×3 or 2 2 × 3 |

## What are the first three common multiples of 8 and 12?

Hence, first four common multiples of 8,12 are 24,48,72,96.

#### What is the LCM of 8?

LCM of 8 and 10 | How to Find LCM of 8 and 10 LCM of 8 and 10 is 40. LCM represents the least common factor or multiple of any two or more given integers. Students can learn the procedure of finding the LCM and HCF of given numbers by referring to anytime for free.

## Do you multiply GCF?

Finding the greatest common factor (Pre-Algebra, Discover fractions and factors) – Mathplanet

- The greatest common factor is exactly as it sounds: the greatest factors of two or more numbers.
- Example
- Find the common factors for 60 and 30

Begin by factoring both numbers. Find all factors that the numbers have in common.

- The product of all common factors is the greatest common factor (GCF)
- $$5\cdot 3\cdot 2=30$$
- The greatest common factor is 30
- Example
- You can also determine the GCF if you have both numbers and variables.
- Find the common factors for 36x 2 y and 16xy

Factorize the numbers and identify all common factors. To get the GCF multiply all common factors.

- You can use the greatest common factor to simplify fractions.
- A ratio is an expression that tells us the quotient of two numbers.
- There are different ways to write a ratio and all examples below are read as “the ratio of 3 to 4”.
- $$3\: to\: 4$$
- $$3:4$$
- $$\frac $$
- $$3\div 4$$
- Example
- You can simplify a ratio by findng the GCF
- $$\frac $$
- Fraction all numbers and find all common factors
- Multiply all common factors to find the GCF
- $$2\cdot 5\cdot 5\cdot 10=500$$
- Since the GCF is a factor of both the numerator and the denominator we can divide both the numerator and the denominator by the GCF to produce a simplified fraction.
- $$\frac =\frac $$

## Can GCF ever be 1?

GCF stands for Greatest Common Factor, You need at least two whole numbers to find the greatest common factor, because the word common here means that we are looking for a factor that two or more numbers share. Since 1 is a factor of every number, any two or more numbers have a GCF, because even if the numbers are prime, or if they don’t share any prime factors, then the GCF will be 1.

## Is 24 the LCM of 8 and 12?

LCM of 8, 12 and 24 | How to Find LCM of 8, 12 and 24 LCM of 8, 12 and 24 is 24, In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 8, 12, and 24 is the LCM of 8, 12, and 24.

## Is 24 a factor of 8 and 12?

Factors of 24 (How to Find Factors and Prime Factorisation of 24) Factors of 24 are the integers that can divide the original uniformly. Thus, there will be no remainder left.24 is a composite number, therefore it will have factors more than two. There are a total of eight factors of 24, they are 1, 2, 3, 4, 6, 8, 12 and 24.

## What is the GCF of 8 and 10?

What is the GCF of 8 and 10? | Thinkster Math The first step to this method of finding the Greatest Common Factor of 8 and 10 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.

Let’s take a look at the factors for each of these numbers, 8 and 10:Factors of 8: 1, 2, 4, 8Factors of 10: 1, 2, 5, 10

When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 8 and 10 would be 2. : What is the GCF of 8 and 10? | Thinkster Math

#### What is GCF and LCM?

Review – Let’s wrap up with a couple of true or false review questions: 1. The least common multiple of 45 and 60 is 15. The answer is false. The greatest common factor of 45 and 60 is 15, but the least common multiple is 180.2. The least common multiple is a number greater than or equal to the numbers being considered.

The answer is true. The least common multiple is greater than or equal to the numbers being considered, while the greatest common factor is equal to or less than the numbers being considered. Thanks for watching, and happy studying! There are a variety of techniques for finding the LCM and GCF. The two most common strategies involve making a list, or using the prime factorization.

For example, the LCM of 5 and 6 can be found by simply listing the multiples of \(5\) and \(6\), and then identifying the lowest multiple shared by both numbers.\(5, 10, 15, 20, 25, \mathbf, 35\) \(6, 12, 18, 24, \mathbf, 36\) \(\mathbf \) is the LCM.

- Similarly, the GCF can be found by listing the factors of each number, and then identifying the greatest factor that is shared.
- For example, the GCF of \(40\) and \(32\) can be found by listing the factors of each number.
- 40\): \(1, 2, 4, 5, \mathbf8, 10, 20, 40\) \(32\): \(1, 2, 4, \mathbf8, 16, 32\) \(\mathbf8\) is the GCF.

For larger numbers, it will not be realistic to make a list of factors or multiples to identify the GCF or LCM. For large numbers, it is most efficient to use the prime factorization technique. For example, when finding the LCM, start by finding the prime factorization of each number (this can be done by creating a factor tree). Now multiply all of the factors (remember not to double-count those circled \(2\)s). This becomes \(2\times2\times5\times2\times2\times2\), which equals \(160\). The LCM of \(20\) and \(32\) is \(160\). When finding the GCF, start by listing the prime factorization of each number (this can be done by creating a factor tree).

- For example, the prime factorization of \(45\) is \(5\times3\times3\), and the prime factorization of \(120\) is \(5\times3\times2\times2\times2\).
- Now simply multiply all of the factors that are shared by both numbers.
- In this case, we would multiply \(5\times3\) which equals \(15\).
- The GCF of \(45\) and \(120\) is \(15\).

The prime factorization approach can seem like a fairly lengthy process, but when working with large numbers it is guaranteed to be a time-saver. There are two main strategies for finding the GCF: Listing the factors, or using the prime factorization.

The first strategy involves simply listing the factors of each number, and then looking for the greatest factor that is shared by both numbers. For example, if we are looking for the GCF of \(36\) and \(45\), we can list the factors of both numbers and identify the largest number in common. \(36\): \(1,2,3,4,6,\mathbf9,12,18,36\) \(45\): \(1,3,5,\mathbf9,15,45\) The GCF of \(36\) and \(45\) is \(\mathbf9\).

Listing the factors of each number and then identifying the largest factor in common works well for small numbers. However, when finding the GCF of very large numbers it is more efficient to use the prime factorization approach. For example, when finding the GCF of \(180\) and \(162\), we start by listing the prime factorization of each number (this can be done by creating a factor tree).

The prime factorization of \(180\) is \(2\times2\times3\times3\times5\), and the prime factorization of \(162\) is \(2\times3\times3\times3\times3\). Now look for the factors that are shared by both numbers. In this case, both numbers share one \(2\), and two \(3\)s, or \(2\times3\times3\). The result of \(2\times3\times3\) is \(18\), which is the GCF! This strategy is often more efficient when finding the GCF of really large numbers.

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of \(24\) and \(36\) is \(12\), because the largest factor that is shared by \(24\) and \(36\) is \(12\).

- 24\) and \(36\) have other factors in common, but \(12\) is the largest.
- There are a variety of techniques for finding the lowest common multiple.
- Two common approaches are listing the multiples, and using the prime factorization.
- Listing the multiples is just as it sounds, simply list the multiples of each number, and then look for the lowest multiple shared by both numbers.

For example, when finding the lowest common multiple of \(3\) and \(4\), list the multiples: \(3\): \(3,6,9,\mathbf,15,18\) \(4\): \(4,8,\mathbf,16,20\) \(\mathbf \) is the lowest multiple shared by \(3\) and \(4\). Listing the multiples is a great strategy when the numbers are fairly small. Now multiply all of the factors (remember to only count the \(2\)s once). This becomes \(2\times19\times3\times7\), which equals \(798\). The LCM of \(38\) and \(42\) is \(798\). Taking out the LCM is a helpful skill when adding or subtracting fractions. Question #1: What is the greatest common factor of 16 and 42? Use it to reduce the fraction \(\frac \). GCF is 8, and we reduce to \(\frac \). GCF is 1, and we cannot reduce any further. GCF is 4, and we reduce to \(\frac \). GCF is 2, and we reduce to \(\frac \). Show Answer Answer:

- The correct answer is D: GCF is 2, and we reduce to \(\frac \).
- Let’s approach this problem by listing the prime factors of both the numerator and the denominator. \(16=2×2×2×2\)
- \(42=2×3×7\)
- Here we see that 2 is the only shared factor of 16 and 42 and is therefore their greatest common factor. We can then divide both numbers by 2 to reduce the fraction: \(\frac =\frac \)

Hide Answer Question #2: Find the least common multiple of 2, 6, and 8. Show Answer Answer:

- The correct answer is C: 24.
- For this problem, let’s list the prime factors of each number. \(2=2\) (note that we could write \(2\times1\), but 1 is understood, or implied, and usually not necessary to write) \(6=2\times3\)
- \(8=2\times2\times2\)

Remember, when calculating the LCM of two or more numbers, we list each prime factor once that is shared by all of the numbers. Since each of our numbers has 2 as a prime factor, our LCM will also have 2 as one of its prime factors. LCM \(=2\times\) _ Now from the 6 we have a leftover 3, and from the 8 we have two 2’s remaining.

We multiply those in to get LCM \(=2\times3\times2\times2=24\) Notice that even though 2, 6, and 8 are all factors of 48, the solution is not D, because 48 is not the smallest common multiple. Hide Answer Question #3: List the first several multiples of 3, 5, and 6 to find the least common multiple. Show Answer Answer: The correct answer is B: LCM is 30.

The first several multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, The first several multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, The first several multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, As we see above, 30 is the first (least) number that 3, 5, and 6 have in common among their multiples, so the least common multiple is 30.

- The correct answer is D: 5 bags, with 18 pieces of candy in each.
- To begin, list the prime factors of both 54 and 36: \(54=2\times3\times3\times3\)
- \(36=2\times2\times3\times3\)

Notice that they both share a 2 and two 3’s. The product of these shared prime factors is \(2\times3\times3=18\). We now know that the GCF is 18, which means each bag will contain 18 pieces of candy. Courtney’s 54 pieces will make 3 bags, and Trish’s 36 pieces will make 2 bags.

- The correct answer is C: 12 apples and 12 bananas.
- With this problem, we want to know the least common multiple of 4 and 6. Using the prime factors method, we see that \(4=2\times2\) \(6=2\times3\)
- LCM \(=2\times2\times3=12\)
- Sara will buy three bags of apples and two bunches of bananas in order to have 12 of each fruit.

Hide Answer 838699 249197 520269 946579 by | This Page Last Updated: February 17, 2023 : What is the Greatest Common Factor and Least Common Multiple?

## What is the LCM GCF of 8 10 and 12?

Hence, the required LCM is LCM 8, 10, 12 = 120.

## Is the GCF of 8 12 and 16?

The greatest common factor 16, 8, 12 is 4.

#### What is the GCF and LCM of 8 12 and 16?

LCM of 8, 12 and 16 is 48.