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

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

Answer: GCF the 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 biggest positive creature m(14) the divides both x(42) and also y(56) without any type of remainder.


The approaches to find the GCF of 42 and 56 are defined below.

Listing common FactorsLong department MethodPrime factorization Method

GCF of 42 and 56 by Listing typical Factors

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

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

GCF of 42 and also 56 by long Division

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

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

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

GCF the 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. Together visible, 42 and 56 have typical prime factors. Hence, the GCF the 42 and 56 is 2 × 7 = 14.

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GCF the 42 and 56 Examples


Example 1: uncover the GCF of 42 and also 56, if their LCM is 168.

Solution:

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


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

Solution:

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


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

Solution:

The best number the divides 42 and 56 specifically is their greatest usual factor, i.e. GCF that 42 and 56.⇒ components of 42 and also 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 the 42 and 56 is 14.


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FAQs on GCF that 42 and also 56

What is the GCF the 42 and 56?

The GCF the 42 and 56 is 14. To calculate the GCF of 42 and also 56, we need to variable each number (factors that 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 aspect that precisely divides both 42 and 56, i.e., 14.

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

The complying with equation have the right to be offered to to express the relation between Least usual Multiple and GCF of 42 and 56, i.e. GCF × LCM = 42 × 56.

What room the methods to discover GCF that 42 and 56?

There are three frequently used techniques to discover the GCF of 42 and 56.

By element FactorizationBy Euclidean AlgorithmBy long Division

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

To uncover the GCF the 42, 56 making use of long division method, 56 is separated by 42. The matching divisor (14) as soon as remainder equals 0 is taken as GCF.

See more: How Many Pounds Is 86 Kg - Convert 86 Kilograms To Pounds

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

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

How to uncover the GCF of 42 and 56 by element Factorization?

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