GCF that 28 and also 42 is the largest possible number that divides 28 and also 42 exactly without any remainder. The components of 28 and 42 are 1, 2, 4, 7, 14, 28 and also 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 frequently used approaches to find the GCF that 28 and 42 - element factorization, lengthy division, and Euclidean algorithm.

You are watching: What is the gcf of 28 and 42

1.GCF that 28 and also 42
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF that 28 and 42 is 14.

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Explanation:

The GCF of two non-zero integers, x(28) and y(42), is the biggest positive creature m(14) the divides both x(28) and y(42) without any remainder.


The methods to find the GCF the 28 and also 42 are explained below.

Listing common FactorsLong division MethodPrime administer Method

GCF of 28 and 42 through Listing common Factors

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

There room 4 common factors the 28 and 42, that room 1, 2, 14, and 7. Therefore, the greatest usual factor of 28 and also 42 is 14.

GCF the 28 and 42 by long Division

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GCF that 28 and also 42 is the divisor the we acquire when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of action 1 (28) by the remainder (14).Step 3: Repeat this process until the remainder = 0.

The equivalent divisor (14) is the GCF that 28 and also 42.

GCF that 28 and 42 by prime Factorization

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Prime administrate of 28 and also 42 is (2 × 2 × 7) and also (2 × 3 × 7) respectively. Together visible, 28 and 42 have typical prime factors. Hence, the GCF of 28 and also 42 is 2 × 7 = 14.

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GCF the 28 and 42 Examples


Example 1: For two numbers, GCF = 14 and LCM = 84. If one number is 28, discover the other number.

Solution:

Given: GCF (x, 28) = 14 and also LCM (x, 28) = 84∵ GCF × LCM = 28 × (x)⇒ x = (GCF × LCM)/28⇒ x = (14 × 84)/28⇒ x = 42Therefore, the various other number is 42.


Example 2: uncover the GCF that 28 and 42, if their LCM is 84.

Solution:

∵ LCM × GCF = 28 × 42⇒ GCF(28, 42) = (28 × 42)/84 = 14Therefore, the greatest common factor of 28 and also 42 is 14.


Example 3: The product of two numbers is 1176. If their GCF is 14, what is your LCM?

Solution:

Given: GCF = 14 and product of number = 1176∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 1176/14Therefore, the LCM is 84.


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FAQs on GCF of 28 and 42

What is the GCF the 28 and also 42?

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

How to discover the GCF that 28 and 42 by Long division Method?

To uncover the GCF that 28, 42 making use of long division method, 42 is separated by 28. The equivalent divisor (14) when remainder amounts to 0 is taken together GCF.

If the GCF of 42 and also 28 is 14, uncover its LCM.

GCF(42, 28) × LCM(42, 28) = 42 × 28Since the GCF of 42 and 28 = 14⇒ 14 × LCM(42, 28) = 1176Therefore, LCM = 84☛ Greatest common Factor Calculator

What is the Relation in between LCM and also GCF the 28, 42?

The following equation can be used to refer the relation in between LCM (Least usual Multiple) and also GCF of 28 and 42, i.e. GCF × LCM = 28 × 42.

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How to discover the GCF of 28 and 42 by element Factorization?

To uncover the GCF that 28 and also 42, we will uncover the prime factorization the the given numbers, i.e. 28 = 2 × 2 × 7; 42 = 2 × 3 × 7.⇒ since 2, 7 are typical terms in the prime factorization that 28 and also 42. Hence, GCF(28, 42) = 2 × 7 = 14☛ prime Number

What room the methods to uncover GCF of 28 and also 42?

There space three generally used methods to discover the GCF that 28 and 42.