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GCF of 12 and 36

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

1.	GCF of 12 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 36?

Answer: GCF of 12 and 36 is 12.

Explanation:

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

Methods to Find GCF of 12 and 36

The methods to find the GCF of 12 and 36 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 12 and 36 by Listing Common Factors

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

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

GCF of 12 and 36 by Prime Factorization

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

GCF of 12 and 36 by Long Division

GCF of 12 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 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the GCF of 12 and 36.

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

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GCF of 12 and 36 Examples

Example 1: Find the GCF of 12 and 36, if their LCM is 36.

Solution:

∵ LCM × GCF = 12 × 36
⇒ GCF(12, 36) = (12 × 36)/36 = 12
Therefore, the greatest common factor of 12 and 36 is 12.
Example 2: The product of two numbers is 432. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 432
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 432/12
Therefore, the LCM is 36.
Example 3: Find the greatest number that divides 12 and 36 exactly.

Solution:

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

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FAQs on GCF of 12 and 36

What is the GCF of 12 and 36?

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

What are the Methods to Find GCF of 12 and 36?

There are three commonly used methods to find the GCF of 12 and 36.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and GCF of 12, 36?

The following equation can be used to express the relation between LCM and GCF of 12 and 36, i.e. GCF × LCM = 12 × 36.

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

GCF(36, 12) × LCM(36, 12) = 36 × 12
Since the GCF of 36 and 12 = 12
⇒ 12 × LCM(36, 12) = 432
Therefore, LCM = 36
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How to Find the GCF of 12 and 36 by Long Division Method?

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

How to Find the GCF of 12 and 36 by Prime Factorization?

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