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GCF of 21 and 63

GCF of 21 and 63 is the largest possible number that divides 21 and 63 exactly without any remainder. The factors of 21 and 63 are 1, 3, 7, 21 and 1, 3, 7, 9, 21, 63 respectively. There are 3 commonly used methods to find the GCF of 21 and 63 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 21 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 63?

Answer: GCF of 21 and 63 is 21.

Explanation:

The GCF of two non-zero integers, x(21) and y(63), is the greatest positive integer m(21) that divides both x(21) and y(63) without any remainder.

Methods to Find GCF of 21 and 63

The methods to find the GCF of 21 and 63 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 21 and 63 by Prime Factorization

Prime factorization of 21 and 63 is (3 × 7) and (3 × 3 × 7) respectively. As visible, 21 and 63 have common prime factors. Hence, the GCF of 21 and 63 is 3 × 7 = 21.

GCF of 21 and 63 by Long Division

GCF of 21 and 63 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 63 (larger number) by 21 (smaller number).
Step 2: Since the remainder = 0, the divisor (21) is the GCF of 21 and 63.

The corresponding divisor (21) is the GCF of 21 and 63.

GCF of 21 and 63 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 63: 1, 3, 7, 9, 21, 63

There are 4 common factors of 21 and 63, that are 1, 3, 21, and 7. Therefore, the greatest common factor of 21 and 63 is 21.

☛ Also Check:

GCF of 21 and 63 Examples

Example 1: Find the GCF of 21 and 63, if their LCM is 63.

Solution:

∵ LCM × GCF = 21 × 63
⇒ GCF(21, 63) = (21 × 63)/63 = 21
Therefore, the greatest common factor of 21 and 63 is 21.
Example 2: For two numbers, GCF = 21 and LCM = 63. If one number is 21, find the other number.

Solution:

Given: GCF (x, 21) = 21 and LCM (x, 21) = 63
∵ GCF × LCM = 21 × (x)
⇒ x = (GCF × LCM)/21
⇒ x = (21 × 63)/21
⇒ x = 63
Therefore, the other number is 63.
Example 3: The product of two numbers is 1323. If their GCF is 21, what is their LCM?

Solution:

Given: GCF = 21 and product of numbers = 1323
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1323/21
Therefore, the LCM is 63.

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FAQs on GCF of 21 and 63

What is the GCF of 21 and 63?

The GCF of 21 and 63 is 21. To calculate the greatest common factor of 21 and 63, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 63 = 1, 3, 7, 9, 21, 63) and choose the greatest factor that exactly divides both 21 and 63, i.e., 21.

How to Find the GCF of 21 and 63 by Long Division Method?

To find the GCF of 21, 63 using long division method, 63 is divided by 21. The corresponding divisor (21) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 21, 63?

The following equation can be used to express the relation between Least Common Multiple and GCF of 21 and 63, i.e. GCF × LCM = 21 × 63.

What are the Methods to Find GCF of 21 and 63?

There are three commonly used methods to find the GCF of 21 and 63.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 21 and 63 by Prime Factorization?

To find the GCF of 21 and 63, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 63 = 3 × 3 × 7.
⇒ Since 3, 7 are common terms in the prime factorization of 21 and 63. Hence, GCF(21, 63) = 3 × 7 = 21
☛ Prime Number

If the GCF of 63 and 21 is 21, Find its LCM.

GCF(63, 21) × LCM(63, 21) = 63 × 21
Since the GCF of 63 and 21 = 21
⇒ 21 × LCM(63, 21) = 1323
Therefore, LCM = 63
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