GCF the 21 and 28 is the largest possible number that divides 21 and also 28 specifically without any remainder. The factors of 21 and 28 are 1, 3, 7, 21 and also 1, 2, 4, 7, 14, 28 respectively. There space 3 generally used approaches to find the GCF of 21 and also 28 - long division, prime factorization, and also Euclidean algorithm.

You are watching: What is the greatest common factor of 21 and 28

1.GCF the 21 and 28
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 21 and 28 is 7.

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Explanation:

The GCF of 2 non-zero integers, x(21) and y(28), is the greatest positive essence m(7) that divides both x(21) and y(28) without any kind of remainder.


The techniques to find the GCF the 21 and also 28 are defined below.

Prime administer MethodUsing Euclid's AlgorithmListing typical Factors

GCF the 21 and also 28 by prime Factorization

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Prime factorization of 21 and 28 is (3 × 7) and (2 × 2 × 7) respectively. Together visible, 21 and 28 have actually only one usual prime variable i.e. 7. Hence, the GCF of 21 and also 28 is 7.

GCF the 21 and also 28 by Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and also mod is the modulo operator.

Here X = 28 and also Y = 21

GCF(28, 21) = GCF(21, 28 mode 21) = GCF(21, 7)GCF(21, 7) = GCF(7, 21 mod 7) = GCF(7, 0)GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF that 21 and 28 is 7.

GCF the 21 and 28 through Listing common Factors

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

There room 2 typical factors the 21 and 28, that are 1 and also 7. Therefore, the greatest common factor that 21 and also 28 is 7.

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GCF that 21 and also 28 Examples


Example 1: find the biggest number the divides 21 and 28 exactly.

Solution:

The biggest number that divides 21 and also 28 exactly is your greatest common factor, i.e. GCF the 21 and also 28.⇒ components of 21 and also 28:

Factors of 21 = 1, 3, 7, 21Factors the 28 = 1, 2, 4, 7, 14, 28

Therefore, the GCF that 21 and also 28 is 7.


Example 2: discover the GCF the 21 and 28, if their LCM is 84.

Solution:

∵ LCM × GCF = 21 × 28⇒ GCF(21, 28) = (21 × 28)/84 = 7Therefore, the greatest typical factor of 21 and also 28 is 7.


Example 3: For two numbers, GCF = 7 and also LCM = 84. If one number is 28, discover the other number.

Solution:

Given: GCF (z, 28) = 7 and LCM (z, 28) = 84∵ GCF × LCM = 28 × (z)⇒ z = (GCF × LCM)/28⇒ z = (7 × 84)/28⇒ z = 21Therefore, the other number is 21.


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FAQs ~ above GCF the 21 and also 28

What is the GCF that 21 and also 28?

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

How to find the GCF that 21 and also 28 by Long department Method?

To discover the GCF of 21, 28 utilizing long department method, 28 is separated by 21. The equivalent divisor (7) once remainder amounts to 0 is taken as GCF.

What are the approaches to discover GCF the 21 and also 28?

There are three typically used techniques to find the GCF the 21 and also 28.

By Euclidean AlgorithmBy long DivisionBy prime Factorization

What is the Relation between LCM and GCF the 21, 28?

The complying with equation have the right to be supplied to refer the relation between Least usual Multiple and also GCF that 21 and 28, i.e. GCF × LCM = 21 × 28.

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How to uncover the GCF of 21 and 28 by prime Factorization?

To discover the GCF that 21 and 28, we will uncover the element factorization that the offered numbers, i.e. 21 = 3 × 7; 28 = 2 × 2 × 7.⇒ because 7 is the only common prime aspect of 21 and also 28. Hence, GCF (21, 28) = 7.☛ element Number

If the GCF of 28 and 21 is 7, discover its LCM.

GCF(28, 21) × LCM(28, 21) = 28 × 21Since the GCF that 28 and 21 = 7⇒ 7 × LCM(28, 21) = 588Therefore, LCM = 84☛ GCF Calculator