GCF the 28 and 42 is the largest feasible number the divides 28 and also 42 specifically without any type of remainder. The components of 28 and 42 space 1, 2, 4, 7, 14, 28 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used approaches to discover the GCF that 28 and also 42 - element factorization, long division, and Euclidean algorithm.

You are watching: Greatest common divisor of 28 and 42

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


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

Listing typical FactorsLong division MethodPrime administrate Method

GCF of 28 and 42 by Listing typical Factors

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

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

GCF the 28 and 42 by lengthy Division

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

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

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

GCF that 28 and 42 by prime Factorization

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Prime factorization 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 the 28 and also 42 is 2 × 7 = 14.

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GCF of 28 and also 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 various other number is 42.


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

Solution:

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


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

Solution:

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


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FAQs top top GCF of 28 and 42

What is the GCF the 28 and 42?

The GCF the 28 and also 42 is 14. To calculation the greatest common factor (GCF) that 28 and 42, we require to aspect 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 variable that specifically divides both 28 and also 42, i.e., 14.

How to uncover the GCF of 28 and 42 by Long department Method?

To discover the GCF that 28, 42 making use of long division method, 42 is separated by 28. The equivalent divisor (14) once remainder equals 0 is taken as GCF.

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

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

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

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

See more: What Is 20 Percent Of 500 Dollars (20% Off $500)? What Is 20 Percent Of 500

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

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

What are the approaches to uncover GCF the 28 and also 42?

There are three frequently used techniques to uncover the GCF that 28 and 42.