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

You are watching: What is the greatest common factor of 28 and 42

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

Answer: GCF that 28 and also 42 is 14.

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Explanation:

The GCF of 2 non-zero integers, x(28) and also y(42), is the biggest positive integer m(14) that divides both x(28) and y(42) without any remainder.


The approaches to discover the GCF that 28 and also 42 are defined below.

Listing usual FactorsLong division MethodPrime administer Method

GCF that 28 and also 42 by Listing common Factors

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

There space 4 typical factors that 28 and also 42, that are 1, 2, 14, and also 7. Therefore, the greatest usual factor the 28 and 42 is 14.

GCF of 28 and 42 by lengthy Division

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GCF that 28 and also 42 is the divisor that we gain when the remainder becomes 0 ~ doing long department repeatedly.

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

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

GCF of 28 and 42 by element Factorization

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

☛ likewise Check:


GCF of 28 and 42 Examples


Example 1: For two numbers, GCF = 14 and also LCM = 84. If one number is 28, uncover 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 other number is 42.


Example 2: find the GCF of 28 and also 42, if their LCM is 84.

Solution:

∵ LCM × GCF = 28 × 42⇒ GCF(28, 42) = (28 × 42)/84 = 14Therefore, the greatest typical 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 also product of number = 1176∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1176/14Therefore, the LCM is 84.


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FAQs ~ above GCF of 28 and 42

What is the GCF of 28 and 42?

The GCF that 28 and also 42 is 14. To calculation the greatest usual factor (GCF) the 28 and also 42, we need to aspect each number (factors the 28 = 1, 2, 4, 7, 14, 28; components 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 the 28 and also 42 through Long department Method?

To find the GCF the 28, 42 making use of long department method, 42 is divided by 28. The corresponding divisor (14) as soon as remainder amounts to 0 is taken as GCF.

If the GCF the 42 and also 28 is 14, discover 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 usual Factor Calculator

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

The adhering to equation can be used to express the relation in between LCM (Least typical Multiple) and also GCF the 28 and 42, i.e. GCF × LCM = 28 × 42.

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

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

What are the techniques to find GCF of 28 and 42?

There space three typically used techniques to find the GCF the 28 and 42.