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GCF of 21 and 36

GCF of 21 and 36 is the largest possible number that divides 21 and 36 exactly without any remainder. The factors of 21 and 36 are 1, 3, 7, 21 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 21 and 36 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 21 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 36?

Answer: GCF of 21 and 36 is 3.

Explanation:

The GCF of two non-zero integers, x(21) and y(36), is the greatest positive integer m(3) that divides both x(21) and y(36) without any remainder.

Methods to Find GCF of 21 and 36

Let's look at the different methods for finding the GCF of 21 and 36.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 21 and 36 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 2 common factors of 21 and 36, that are 1 and 3. Therefore, the greatest common factor of 21 and 36 is 3.

GCF of 21 and 36 by Prime Factorization

Prime factorization of 21 and 36 is (3 × 7) and (2 × 2 × 3 × 3) respectively. As visible, 21 and 36 have only one common prime factor i.e. 3. Hence, the GCF of 21 and 36 is 3.

GCF of 21 and 36 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 = 36 and Y = 21

GCF(36, 21) = GCF(21, 36 mod 21) = GCF(21, 15)
GCF(21, 15) = GCF(15, 21 mod 15) = GCF(15, 6)
GCF(15, 6) = GCF(6, 15 mod 6) = GCF(6, 3)
GCF(6, 3) = GCF(3, 6 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 21 and 36 is 3.

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GCF of 21 and 36 Examples

Example 1: Find the greatest number that divides 21 and 36 exactly.

Solution:

The greatest number that divides 21 and 36 exactly is their greatest common factor, i.e. GCF of 21 and 36.
⇒ Factors of 21 and 36:
- Factors of 21 = 1, 3, 7, 21
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 21 and 36 is 3.
Example 2: Find the GCF of 21 and 36, if their LCM is 252.

Solution:

∵ LCM × GCF = 21 × 36
⇒ GCF(21, 36) = (21 × 36)/252 = 3
Therefore, the greatest common factor of 21 and 36 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 252. If one number is 36, find the other number.

Solution:

Given: GCF (y, 36) = 3 and LCM (y, 36) = 252
∵ GCF × LCM = 36 × (y)
⇒ y = (GCF × LCM)/36
⇒ y = (3 × 252)/36
⇒ y = 21
Therefore, the other number is 21.

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FAQs on GCF of 21 and 36

What is the GCF of 21 and 36?

The GCF of 21 and 36 is 3. To calculate the GCF (Greatest Common Factor) of 21 and 36, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 21 and 36, i.e., 3.

How to Find the GCF of 21 and 36 by Prime Factorization?

To find the GCF of 21 and 36, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 36 = 2 × 2 × 3 × 3.
⇒ Since 3 is the only common prime factor of 21 and 36. Hence, GCF (21, 36) = 3.
☛ What is a Prime Number?

How to Find the GCF of 21 and 36 by Long Division Method?

To find the GCF of 21, 36 using long division method, 36 is divided by 21. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 21 and 36?

There are three commonly used methods to find the GCF of 21 and 36.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and GCF of 21, 36?

The following equation can be used to express the relation between LCM and GCF of 21 and 36, i.e. GCF × LCM = 21 × 36.

If the GCF of 36 and 21 is 3, Find its LCM.

GCF(36, 21) × LCM(36, 21) = 36 × 21
Since the GCF of 36 and 21 = 3
⇒ 3 × LCM(36, 21) = 756
Therefore, LCM = 252
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