GCF of 21 and 28 is the largest feasible number that divides 21 and also 28 specifically without any remainder. The factors of 21 and also 28 space 1, 3, 7, 21 and also 1, 2, 4, 7, 14, 28 respectively. There room 3 typically used methods to discover the GCF that 21 and 28 - lengthy division, prime factorization, and also Euclidean algorithm.

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1.GCF of 21 and also 28
2.List that 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 also y(28), is the best positive essence m(7) the divides both x(21) and also y(28) without any remainder.


The techniques to discover the GCF the 21 and 28 are described below.

Prime administrate MethodUsing Euclid's AlgorithmListing typical Factors

GCF the 21 and 28 by element Factorization

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Prime administer of 21 and also 28 is (3 × 7) and also (2 × 2 × 7) respectively. As visible, 21 and also 28 have only one common prime aspect i.e. 7. Hence, the GCF that 21 and also 28 is 7.

GCF of 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 Y = 21

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

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

GCF of 21 and also 28 by Listing typical Factors

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

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

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GCF of 21 and 28 Examples


Example 1: uncover the best number that divides 21 and also 28 exactly.

Solution:

The biggest number the divides 21 and 28 specifically is their greatest typical factor, i.e. GCF the 21 and also 28.⇒ factors of 21 and also 28:

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

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


Example 2: uncover the GCF that 21 and 28, if your LCM is 84.

Solution:

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


Example 3: For 2 numbers, GCF = 7 and also LCM = 84. If one number is 28, uncover the various 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 various other number is 21.


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FAQs ~ above GCF that 21 and 28

What is the GCF of 21 and 28?

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

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

To uncover the GCF that 21, 28 utilizing long department method, 28 is separated by 21. The corresponding divisor (7) once remainder equals 0 is taken as GCF.

What are the techniques to discover GCF that 21 and also 28?

There space three typically used methods to find the GCF the 21 and 28.

By Euclidean AlgorithmBy lengthy DivisionBy element Factorization

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

The following equation can be used to to express the relation in between Least typical Multiple and also GCF that 21 and 28, i.e. GCF × LCM = 21 × 28.

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

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

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

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