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

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

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

Answer: GCF of 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 creature m(7) the divides both x(21) and also y(28) without any kind of remainder.


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

Prime administrate MethodUsing Euclid's AlgorithmListing common Factors

GCF of 21 and 28 by element 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 common prime factor i.e. 7. Hence, the GCF of 21 and 28 is 7.

GCF that 21 and 28 by Euclidean Algorithm

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

Here X = 28 and Y = 21

GCF(28, 21) = GCF(21, 28 mode 21) = GCF(21, 7)GCF(21, 7) = GCF(7, 21 mode 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 that 21 and also 28 by Listing usual Factors

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

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

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GCF of 21 and 28 Examples


Example 1: discover the greatest number that divides 21 and also 28 exactly.

Solution:

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

Factors that 21 = 1, 3, 7, 21Factors that 28 = 1, 2, 4, 7, 14, 28

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


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

Solution:

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


Example 3: For 2 numbers, GCF = 7 and 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 various other number is 21.


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FAQs top top GCF the 21 and also 28

What is the GCF that 21 and 28?

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

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

To discover the GCF the 21, 28 using long department method, 28 is separated by 21. The corresponding divisor (7) as soon as remainder equals 0 is taken together GCF.

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

There are three typically used approaches to uncover the GCF the 21 and also 28.

By Euclidean AlgorithmBy long DivisionBy element Factorization

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

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

See more: What Is The Formula For Zinc Sulfide (Zns) Semiconductors, Zinc Sulfide

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

To find the GCF that 21 and also 28, we will find the element factorization that the given numbers, i.e. 21 = 3 × 7; 28 = 2 × 2 × 7.⇒ because 7 is the only typical prime factor of 21 and 28. Hence, GCF (21, 28) = 7.☛ prime Number

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

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