GCF of 28 and 42 is the largest possible number that divides 28 and 42 exactly without any remainder. The factors of 28 and 42 are 1, 2, 4, 7, 14, 28 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 28 and 42 - prime factorization, long division, and Euclidean algorithm.

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

Answer: GCF of 28 and 42 is 14.

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Explanation:

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


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

Listing Common FactorsLong Division MethodPrime Factorization Method

GCF of 28 and 42 by Listing Common Factors

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

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

GCF of 28 and 42 by Long Division

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GCF of 28 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (14).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the GCF of 28 and 42.

GCF of 28 and 42 by Prime Factorization

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Prime factorization of 28 and 42 is (2 × 2 × 7) and (2 × 3 × 7) respectively. As visible, 28 and 42 have common prime factors. Hence, the GCF of 28 and 42 is 2 × 7 = 14.

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GCF of 28 and 42 Examples


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

Solution:

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


Example 2: Find the GCF of 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 42 is 14.


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

Solution:

Given: GCF = 14 and product of numbers = 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 of 28 and 42?

The GCF of 28 and 42 is 14. To calculate the greatest common factor (GCF) of 28 and 42, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 28 and 42, i.e., 14.

How to Find the GCF of 28 and 42 by Long Division Method?

To find the GCF of 28, 42 using long division method, 42 is divided by 28. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

If the GCF of 42 and 28 is 14, Find 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 Between LCM and GCF of 28, 42?

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

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How to Find the GCF of 28 and 42 by Prime Factorization?

To find the GCF of 28 and 42, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 42 = 2 × 3 × 7.⇒ Since 2, 7 are common terms in the prime factorization of 28 and 42. Hence, GCF(28, 42) = 2 × 7 = 14☛ Prime Number

What are the Methods to Find GCF of 28 and 42?

There are three commonly used methods to find the GCF of 28 and 42.