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GCF of 21 and 24

GCF of 21 and 24 is the largest possible number that divides 21 and 24 exactly without any remainder. The factors of 21 and 24 are 1, 3, 7, 21 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 21 and 24 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 21 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 24?

Answer: GCF of 21 and 24 is 3.

Explanation:

The GCF of two non-zero integers, x(21) and y(24), is the greatest positive integer m(3) that divides both x(21) and y(24) without any remainder.

Methods to Find GCF of 21 and 24

The methods to find the GCF of 21 and 24 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 21 and 24 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 = 24 and Y = 21

GCF(24, 21) = GCF(21, 24 mod 21) = GCF(21, 3)
GCF(21, 3) = GCF(3, 21 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 21 and 24 is 3.

GCF of 21 and 24 by Prime Factorization

Prime factorization of 21 and 24 is (3 × 7) and (2 × 2 × 2 × 3) respectively. As visible, 21 and 24 have only one common prime factor i.e. 3. Hence, the GCF of 21 and 24 is 3.

GCF of 21 and 24 by Long Division

GCF of 21 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 21 and 24.

☛ Also Check:

GCF of 21 and 24 Examples

Example 1: Find the greatest number that divides 21 and 24 exactly.

Solution:

The greatest number that divides 21 and 24 exactly is their greatest common factor, i.e. GCF of 21 and 24.
⇒ Factors of 21 and 24:
- Factors of 21 = 1, 3, 7, 21
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 21 and 24 is 3.
Example 2: For two numbers, GCF = 3 and LCM = 168. If one number is 21, find the other number.

Solution:

Given: GCF (z, 21) = 3 and LCM (z, 21) = 168
∵ GCF × LCM = 21 × (z)
⇒ z = (GCF × LCM)/21
⇒ z = (3 × 168)/21
⇒ z = 24
Therefore, the other number is 24.
Example 3: Find the GCF of 21 and 24, if their LCM is 168.

Solution:

∵ LCM × GCF = 21 × 24
⇒ GCF(21, 24) = (21 × 24)/168 = 3
Therefore, the greatest common factor of 21 and 24 is 3.

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FAQs on GCF of 21 and 24

What is the GCF of 21 and 24?

The GCF of 21 and 24 is 3. To calculate the greatest common factor of 21 and 24, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 21 and 24, i.e., 3.

If the GCF of 24 and 21 is 3, Find its LCM.

GCF(24, 21) × LCM(24, 21) = 24 × 21
Since the GCF of 24 and 21 = 3
⇒ 3 × LCM(24, 21) = 504
Therefore, LCM = 168
☛ Greatest Common Factor Calculator

How to Find the GCF of 21 and 24 by Prime Factorization?

To find the GCF of 21 and 24, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 24 = 2 × 2 × 2 × 3.
⇒ Since 3 is the only common prime factor of 21 and 24. Hence, GCF (21, 24) = 3.
☛ Prime Number

What are the Methods to Find GCF of 21 and 24?

There are three commonly used methods to find the GCF of 21 and 24.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 21 and 24 by Long Division Method?

To find the GCF of 21, 24 using long division method, 24 is divided by 21. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 21, 24?

The following equation can be used to express the relation between LCM and GCF of 21 and 24, i.e. GCF × LCM = 21 × 24.

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