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GCF of 24 and 36

GCF of 24 and 36 is the largest possible number that divides 24 and 36 exactly without any remainder. The factors of 24 and 36 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 24 and 36 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 24 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 24 and 36?

Answer: GCF of 24 and 36 is 12.

Explanation:

The GCF of two non-zero integers, x(24) and y(36), is the greatest positive integer m(12) that divides both x(24) and y(36) without any remainder.

Methods to Find GCF of 24 and 36

Let's look at the different methods for finding the GCF of 24 and 36.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 24 and 36 by Prime Factorization

Prime factorization of 24 and 36 is (2 × 2 × 2 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 24 and 36 have common prime factors. Hence, the GCF of 24 and 36 is 2 × 2 × 3 = 12.

GCF of 24 and 36 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 6 common factors of 24 and 36, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 24 and 36 is 12.

GCF of 24 and 36 by Long Division

GCF of 24 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 24 and 36.

☛ Also Check:

GCF of 24 and 36 Examples

Example 1: The product of two numbers is 864. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 864
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 864/12
Therefore, the LCM is 72.
Example 2: Find the GCF of 24 and 36, if their LCM is 72.

Solution:

∵ LCM × GCF = 24 × 36
⇒ GCF(24, 36) = (24 × 36)/72 = 12
Therefore, the greatest common factor of 24 and 36 is 12.
Example 3: Find the greatest number that divides 24 and 36 exactly.

Solution:

The greatest number that divides 24 and 36 exactly is their greatest common factor, i.e. GCF of 24 and 36.
⇒ Factors of 24 and 36:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 24 and 36 is 12.

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FAQs on GCF of 24 and 36

What is the GCF of 24 and 36?

The GCF of 24 and 36 is 12. To calculate the GCF (Greatest Common Factor) of 24 and 36, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 24 and 36, i.e., 12.

What is the Relation Between LCM and GCF of 24, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 24 and 36, i.e. GCF × LCM = 24 × 36.

How to Find the GCF of 24 and 36 by Prime Factorization?

To find the GCF of 24 and 36, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 24 and 36. Hence, GCF(24, 36) = 2 × 2 × 3 = 12
☛ Prime Numbers

If the GCF of 36 and 24 is 12, Find its LCM.

GCF(36, 24) × LCM(36, 24) = 36 × 24
Since the GCF of 36 and 24 = 12
⇒ 12 × LCM(36, 24) = 864
Therefore, LCM = 72
☛ Greatest Common Factor Calculator

How to Find the GCF of 24 and 36 by Long Division Method?

To find the GCF of 24, 36 using long division method, 36 is divided by 24. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 24 and 36?

There are three commonly used methods to find the GCF of 24 and 36.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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