GCF of 42 and also 56 is the largest possible number the divides 42 and 56 specifically without any 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 space 3 frequently used techniques to find the GCF of 42 and also 56 - prime factorization, Euclidean algorithm, and also long division.

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

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

Answer: GCF that 42 and also 56 is 14.

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Explanation:

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


The approaches to discover the GCF the 42 and also 56 are described below.

Listing common FactorsLong department MethodPrime administer Method

GCF of 42 and also 56 by Listing common Factors

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

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

GCF that 42 and 56 by lengthy Division

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

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

The corresponding divisor (14) is the GCF the 42 and 56.

GCF the 42 and also 56 by prime Factorization

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

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GCF that 42 and 56 Examples


Example 1: find the GCF the 42 and also 56, if your LCM is 168.

Solution:

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


Example 2: The product of 2 numbers is 2352. If their 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 greatest number the divides 42 and 56 exactly.

Solution:

The greatest number that divides 42 and 56 specifically is their greatest typical factor, i.e. GCF the 42 and also 56.⇒ factors of 42 and also 56:

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

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


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FAQs top top GCF that 42 and also 56

What is the GCF the 42 and 56?

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

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

The following equation have the right to be supplied to refer the relation in between Least usual Multiple and GCF of 42 and 56, i.e. GCF × LCM = 42 × 56.

What are the approaches to uncover GCF the 42 and 56?

There space three typically used methods to find the GCF of 42 and 56.

By element FactorizationBy Euclidean AlgorithmBy long Division

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

To find the GCF of 42, 56 making use of long division method, 56 is separated by 42. The equivalent divisor (14) as soon as remainder equates to 0 is taken as GCF.

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If the GCF the 56 and also 42 is 14, find its LCM.

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

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

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