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GCF of 36 and 60

GCF of 36 and 60 is the largest possible number that divides 36 and 60 exactly without any remainder. The factors of 36 and 60 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 36 and 60 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 36 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 60?

Answer: GCF of 36 and 60 is 12.

Explanation:

The GCF of two non-zero integers, x(36) and y(60), is the greatest positive integer m(12) that divides both x(36) and y(60) without any remainder.

Methods to Find GCF of 36 and 60

Let's look at the different methods for finding the GCF of 36 and 60.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 36 and 60 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 6 common factors of 36 and 60, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 60 is 12.

GCF of 36 and 60 by Long Division

GCF of 36 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 36 and 60.

GCF of 36 and 60 by Prime Factorization

Prime factorization of 36 and 60 is (2 × 2 × 3 × 3) and (2 × 2 × 3 × 5) respectively. As visible, 36 and 60 have common prime factors. Hence, the GCF of 36 and 60 is 2 × 2 × 3 = 12.

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GCF of 36 and 60 Examples

Example 1: Find the GCF of 36 and 60, if their LCM is 180.

Solution:

∵ LCM × GCF = 36 × 60
⇒ GCF(36, 60) = (36 × 60)/180 = 12
Therefore, the greatest common factor of 36 and 60 is 12.
Example 2: The product of two numbers is 2160. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 2160
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2160/12
Therefore, the LCM is 180.
Example 3: For two numbers, GCF = 12 and LCM = 180. If one number is 60, find the other number.

Solution:

Given: GCF (z, 60) = 12 and LCM (z, 60) = 180
∵ GCF × LCM = 60 × (z)
⇒ z = (GCF × LCM)/60
⇒ z = (12 × 180)/60
⇒ z = 36
Therefore, the other number is 36.

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FAQs on GCF of 36 and 60

What is the GCF of 36 and 60?

The GCF of 36 and 60 is 12. To calculate the greatest common factor of 36 and 60, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 36 and 60, i.e., 12.

How to Find the GCF of 36 and 60 by Long Division Method?

To find the GCF of 36, 60 using long division method, 60 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

How to Find the GCF of 36 and 60 by Prime Factorization?

To find the GCF of 36 and 60, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 60. Hence, GCF(36, 60) = 2 × 2 × 3 = 12
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 36, 60?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 36 and 60, i.e. GCF × LCM = 36 × 60.

If the GCF of 60 and 36 is 12, Find its LCM.

GCF(60, 36) × LCM(60, 36) = 60 × 36
Since the GCF of 60 and 36 = 12
⇒ 12 × LCM(60, 36) = 2160
Therefore, LCM = 180
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What are the Methods to Find GCF of 36 and 60?

There are three commonly used methods to find the GCF of 36 and 60.

By Long Division
By Euclidean Algorithm
By Prime Factorization

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