GCF of 28 and 42 is the largest feasible number the divides 28 and also 42 specifically without any kind of remainder. The components of 28 and 42 room 1, 2, 4, 7, 14, 28 and also 1, 2, 3, 6, 7, 14, 21, 42 respectively. There room 3 commonly used techniques to uncover the GCF the 28 and also 42 - element factorization, lengthy division, and Euclidean algorithm.

You are watching: Greatest common factor of 28 and 42

1.GCF of 28 and also 42
2.List the 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 also y(42), is the best positive integer m(14) that divides both x(28) and y(42) without any remainder.


The approaches to uncover the GCF that 28 and 42 are explained below.

Listing common FactorsLong department MethodPrime administer Method

GCF that 28 and also 42 by Listing usual Factors

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

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

GCF the 28 and also 42 by lengthy Division

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GCF the 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 procedure until the remainder = 0.

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

GCF of 28 and 42 by prime Factorization

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

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GCF that 28 and also 42 Examples


Example 1: For 2 numbers, GCF = 14 and LCM = 84. If one number is 28, find the various 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 various other number is 42.


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

Solution:

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


Example 3: The product of 2 numbers is 1176. If your GCF is 14, what is their LCM?

Solution:

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


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FAQs on GCF that 28 and 42

What is the GCF that 28 and also 42?

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

How to discover the GCF that 28 and 42 through Long department Method?

To uncover the GCF that 28, 42 using long division method, 42 is separated by 28. The equivalent divisor (14) as soon as remainder equates to 0 is taken together GCF.

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

GCF(42, 28) × LCM(42, 28) = 42 × 28Since the GCF the 42 and also 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 following equation can be supplied to express the relation between LCM (Least typical Multiple) and also GCF of 28 and also 42, i.e. GCF × LCM = 28 × 42.

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

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

What room the methods to discover GCF that 28 and also 42?

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