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GCF of 21 and 28

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

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

What is GCF of 21 and 28?

Answer: GCF of 21 and 28 is 7.

Explanation:

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

Methods to Find GCF of 21 and 28

The methods to find the GCF of 21 and 28 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 21 and 28 by Prime Factorization

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

GCF of 21 and 28 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and 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|, where X ≠ 0)

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

GCF of 21 and 28 by Listing Common Factors

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

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

☛ Also Check:

GCF of 21 and 28 Examples

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

Solution:

The greatest number that divides 21 and 28 exactly is their greatest common factor, i.e. GCF of 21 and 28.
⇒ Factors of 21 and 28:
- Factors of 21 = 1, 3, 7, 21
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 21 and 28 is 7.
Example 2: Find the GCF of 21 and 28, if their LCM is 84.

Solution:

∵ LCM × GCF = 21 × 28
⇒ GCF(21, 28) = (21 × 28)/84 = 7
Therefore, the greatest common factor of 21 and 28 is 7.
Example 3: For two numbers, GCF = 7 and LCM = 84. If one number is 28, find 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 = 21
Therefore, the other number is 21.

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FAQs on GCF of 21 and 28

What is the GCF of 21 and 28?

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

How to Find the GCF of 21 and 28 by Long Division Method?

To find the GCF of 21, 28 using long division method, 28 is divided by 21. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 21 and 28?

There are three commonly used methods to find the GCF of 21 and 28.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 21, 28?

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

How to Find the GCF of 21 and 28 by Prime Factorization?

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

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

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