GCF the 42 and also 56 is the largest possible number that divides 42 and 56 precisely without any type of remainder. The components of 42 and 56 room 1, 2, 3, 6, 7, 14, 21, 42 and also 1, 2, 4, 7, 8, 14, 28, 56 respectively. There room 3 frequently used methods to uncover the GCF the 42 and 56 - prime factorization, Euclidean algorithm, and also long division.

You are watching: What is the gcf of 42 and 56

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

Answer: GCF that 42 and also 56 is 14.

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Explanation:

The GCF of 2 non-zero integers, x(42) and also y(56), is the best positive integer m(14) the divides both x(42) and also y(56) without any kind of remainder.


The techniques to uncover the GCF of 42 and 56 are defined below.

Listing usual FactorsLong division MethodPrime administrate Method

GCF of 42 and also 56 by Listing common Factors

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

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

GCF of 42 and 56 by lengthy Division

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GCF that 42 and 56 is the divisor the we acquire when the remainder i do not care 0 ~ doing long department repeatedly.

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

The matching divisor (14) is the GCF that 42 and also 56.

GCF that 42 and 56 by prime Factorization

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

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GCF of 42 and 56 Examples


Example 1: uncover the GCF the 42 and also 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 two numbers is 2352. If their GCF is 14, what is your LCM?

Solution:

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


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

Solution:

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

Factors that 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 56 is 14.


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FAQs ~ above GCF that 42 and 56

What is the GCF the 42 and 56?

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

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

The adhering to equation can be supplied to express the relation between Least common Multiple and GCF of 42 and 56, i.e. GCF × LCM = 42 × 56.

What room the techniques to discover GCF of 42 and 56?

There space three generally used approaches to uncover the GCF that 42 and also 56.

By element FactorizationBy Euclidean AlgorithmBy long Division

How to uncover the GCF that 42 and 56 by Long department Method?

To find the GCF of 42, 56 utilizing long department method, 56 is split by 42. The equivalent divisor (14) as soon as remainder amounts to 0 is taken together GCF.

See more: How To Do Cotangent On Ti 84 Plus, Secant, Cosecant, And Cotangent On The Ti

If the GCF that 56 and 42 is 14, uncover 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 common Factor Calculator

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

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