GCF the 8 and 12 is the largest possible number that divides 8 and also 12 specifically without any kind of remainder. The factors of 8 and also 12 space 1, 2, 4, 8 and 1, 2, 3, 4, 6, 12 respectively. There space 3 frequently used techniques to discover the GCF of 8 and also 12 - lengthy division, prime factorization, and Euclidean algorithm.

You are watching: Find the gcf of 8 and 12

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

Answer: GCF that 8 and 12 is 4.

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Explanation:

The GCF of 2 non-zero integers, x(8) and also y(12), is the greatest positive integer m(4) that divides both x(8) and also y(12) without any remainder.


The approaches to uncover the GCF of 8 and also 12 are explained below.

Listing common FactorsPrime factorization MethodLong division Method

GCF of 8 and 12 by Listing typical Factors

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

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

GCF that 8 and 12 by prime Factorization

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Prime administrate of 8 and also 12 is (2 × 2 × 2) and (2 × 2 × 3) respectively. Together visible, 8 and also 12 have usual prime factors. Hence, the GCF that 8 and also 12 is 2 × 2 = 4.

GCF the 8 and also 12 by long Division

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

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

The matching divisor (4) is the GCF that 8 and also 12.

☛ likewise Check:


GCF of 8 and 12 Examples


Example 1: The product of 2 numbers is 96. If your GCF is 4, what is your LCM?

Solution:

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


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

Solution:

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


Example 3: For 2 numbers, GCF = 4 and LCM = 24. If one number is 8, discover 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 various other number is 12.


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FAQs ~ above GCF that 8 and also 12

What is the GCF the 8 and also 12?

The GCF the 8 and also 12 is 4. To calculation the GCF of 8 and 12, we require to element each number (factors the 8 = 1, 2, 4, 8; determinants of 12 = 1, 2, 3, 4, 6, 12) and also choose the greatest element that specifically divides both 8 and 12, i.e., 4.

What is the Relation between LCM and also GCF the 8, 12?

The adhering to equation can be provided to to express the relation between LCM and GCF that 8 and also 12, i.e. GCF × LCM = 8 × 12.

How to find the GCF that 8 and also 12 through Long department Method?

To uncover the GCF that 8, 12 using long division method, 12 is separated by 8. The matching divisor (4) once remainder equates to 0 is taken as GCF.

What room the techniques to find GCF the 8 and 12?

There space three generally used techniques to find the GCF that 8 and also 12.

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By long DivisionBy element FactorizationBy Euclidean Algorithm

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

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

How to discover the GCF the 8 and also 12 by element Factorization?

To uncover the GCF of 8 and also 12, us will discover the prime factorization that the provided numbers, i.e. 8 = 2 × 2 × 2; 12 = 2 × 2 × 3.⇒ since 2, 2 are common terms in the prime factorization the 8 and also 12. Hence, GCF(8, 12) = 2 × 2 = 4☛ What is a prime Number?