GCF of 8 and 12 is the largest possible number that divides 8 and 12 exactly without any remainder. The factors of 8 and 12 are 1, 2, 4, 8 and 1, 2, 3, 4, 6, 12 respectively. There are 3 commonly used methods to find the GCF of 8 and 12 - long division, prime factorization, and Euclidean algorithm.

You are watching: Highest common factor of 8 and 12

1.GCF of 8 and 12
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 8 and 12 is 4.

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Explanation:

The GCF of two non-zero integers, x(8) and y(12), is the greatest positive integer m(4) that divides both x(8) and y(12) without any remainder.


The methods to find the GCF of 8 and 12 are explained below.

Listing Common FactorsPrime Factorization MethodLong Division Method

GCF of 8 and 12 by Listing Common Factors

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Factors of 8: 1, 2, 4, 8Factors 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.

GCF of 8 and 12 by Prime Factorization

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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 GCF of 8 and 12 is 2 × 2 = 4.

GCF of 8 and 12 by Long Division

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GCF of 8 and 12 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (4).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 8 and 12.

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GCF of 8 and 12 Examples


Example 1: The product of two numbers is 96. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 96∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 96/4Therefore, the LCM is 24.


Example 2: Find the GCF of 8 and 12, if their LCM is 24.

Solution:

∵ LCM × GCF = 8 × 12⇒ GCF(8, 12) = (8 × 12)/24 = 4Therefore, the greatest common factor of 8 and 12 is 4.


Example 3: For two numbers, GCF = 4 and LCM = 24. If one number is 8, find the other number.

Solution:

Given: GCF (y, 8) = 4 and LCM (y, 8) = 24∵ GCF × LCM = 8 × (y)⇒ y = (GCF × LCM)/8⇒ y = (4 × 24)/8⇒ y = 12Therefore, the other number is 12.


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FAQs on GCF of 8 and 12

What is the GCF of 8 and 12?

The GCF of 8 and 12 is 4. To calculate the GCF of 8 and 12, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 12 = 1, 2, 3, 4, 6, 12) and choose the greatest factor that exactly divides both 8 and 12, i.e., 4.

What is the Relation Between LCM and GCF of 8, 12?

The following equation can be used to express the relation between LCM and GCF of 8 and 12, i.e. GCF × LCM = 8 × 12.

How to Find the GCF of 8 and 12 by Long Division Method?

To find the GCF of 8, 12 using long division method, 12 is divided by 8. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 8 and 12?

There are three commonly used methods to find the GCF of 8 and 12.

See more: Greatest 5 Digit Number Without Repeating Any Digit, What Is The Largest 5

By Long DivisionBy Prime FactorizationBy Euclidean Algorithm

If the GCF of 12 and 8 is 4, Find its LCM.

GCF(12, 8) × LCM(12, 8) = 12 × 8Since the GCF of 12 and 8 = 4⇒ 4 × LCM(12, 8) = 96Therefore, LCM = 24☛ GCF Calculator

How to Find the GCF of 8 and 12 by Prime Factorization?

To find the GCF of 8 and 12, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 12 = 2 × 2 × 3.⇒ Since 2, 2 are common terms in the prime factorization of 8 and 12. Hence, GCF(8, 12) = 2 × 2 = 4☛ What is a Prime Number?