GCF that 42 and 56 is the largest possible number that divides 42 and 56 precisely without any type of remainder. The factors of 42 and also 56 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 4, 7, 8, 14, 28, 56 respectively. There are 3 generally used approaches to find the GCF the 42 and 56 - element factorization, Euclidean algorithm, and long division.

You are watching: What is the greatest common factor of 42 and 56

1.GCF of 42 and 56
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 42 and also 56 is 14.

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Explanation:

The GCF of two non-zero integers, x(42) and also y(56), is the biggest positive essence m(14) that divides both x(42) and also y(56) without any type of remainder.


The methods to find the GCF of 42 and 56 are explained below.

Listing common FactorsLong department MethodPrime administer Method

GCF of 42 and 56 through Listing usual Factors

Factors that 42: 1, 2, 3, 6, 7, 14, 21, 42Factors that 56: 1, 2, 4, 7, 8, 14, 28, 56

There space 4 usual factors that 42 and also 56, that space 1, 2, 14, and 7. Therefore, the greatest typical factor the 42 and also 56 is 14.

GCF that 42 and also 56 by lengthy Division

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GCF that 42 and 56 is the divisor the we obtain when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: because the remainder ≠ 0, we will divide the divisor of step 1 (42) through the remainder (14).Step 3: Repeat this procedure until the remainder = 0.

The equivalent divisor (14) is the GCF of 42 and also 56.

GCF of 42 and also 56 by prime Factorization

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Prime administrate of 42 and also 56 is (2 × 3 × 7) and also (2 × 2 × 2 × 7) respectively. As visible, 42 and also 56 have common prime factors. Hence, the GCF that 42 and 56 is 2 × 7 = 14.

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GCF the 42 and 56 Examples


Example 1: discover the GCF that 42 and 56, if their LCM is 168.

Solution:

∵ LCM × GCF = 42 × 56⇒ GCF(42, 56) = (42 × 56)/168 = 14Therefore, the greatest common factor the 42 and also 56 is 14.


Example 2: The product of 2 numbers is 2352. If your GCF is 14, what is their LCM?

Solution:

Given: GCF = 14 and product of number = 2352∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 2352/14Therefore, the LCM is 168.


Example 3: uncover the biggest number that divides 42 and also 56 exactly.

Solution:

The best number the divides 42 and 56 exactly is your greatest common factor, i.e. GCF that 42 and also 56.⇒ factors of 42 and also 56:

Factors the 42 = 1, 2, 3, 6, 7, 14, 21, 42Factors the 56 = 1, 2, 4, 7, 8, 14, 28, 56

Therefore, the GCF that 42 and also 56 is 14.


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FAQs on GCF that 42 and 56

What is the GCF that 42 and 56?

The GCF the 42 and 56 is 14. To calculation the GCF that 42 and also 56, we require to element each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56) and also choose the greatest aspect that precisely divides both 42 and 56, i.e., 14.

What is the Relation between LCM and also GCF the 42, 56?

The adhering to equation deserve to be used to to express the relation in between Least typical Multiple and also GCF that 42 and also 56, i.e. GCF × LCM = 42 × 56.

What are the methods to find GCF that 42 and 56?

There space three typically used approaches to discover the GCF the 42 and 56.

By prime FactorizationBy Euclidean AlgorithmBy long Division

How to uncover the GCF the 42 and also 56 by Long division Method?

To uncover the GCF the 42, 56 utilizing long division method, 56 is separated by 42. The matching divisor (14) as soon as remainder amounts to 0 is taken together GCF.

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If the GCF that 56 and 42 is 14, discover its LCM.

GCF(56, 42) × LCM(56, 42) = 56 × 42Since the GCF of 56 and 42 = 14⇒ 14 × LCM(56, 42) = 2352Therefore, LCM = 168☛ Greatest typical Factor Calculator

How to discover the GCF the 42 and also 56 by prime Factorization?

To find the GCF the 42 and also 56, us will uncover the prime factorization the the offered numbers, i.e. 42 = 2 × 3 × 7; 56 = 2 × 2 × 2 × 7.⇒ since 2, 7 are typical terms in the prime factorization the 42 and also 56. Hence, GCF(42, 56) = 2 × 7 = 14☛ element Numbers