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GCF of 36 and 120

GCF of 36 and 120 is the largest possible number that divides 36 and 120 exactly without any remainder. The factors of 36 and 120 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 36 and 120 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 36 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 120?

Answer: GCF of 36 and 120 is 12.

Explanation:

The GCF of two non-zero integers, x(36) and y(120), is the greatest positive integer m(12) that divides both x(36) and y(120) without any remainder.

Methods to Find GCF of 36 and 120

The methods to find the GCF of 36 and 120 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 36 and 120 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 = 120 and Y = 36

GCF(120, 36) = GCF(36, 120 mod 36) = GCF(36, 12)
GCF(36, 12) = GCF(12, 36 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 120 is 12.

GCF of 36 and 120 by Long Division

GCF of 36 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 36 and 120.

GCF of 36 and 120 by Prime Factorization

Prime factorization of 36 and 120 is (2 × 2 × 3 × 3) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 36 and 120 have common prime factors. Hence, the GCF of 36 and 120 is 2 × 2 × 3 = 12.

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GCF of 36 and 120 Examples

Example 1: The product of two numbers is 4320. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 4320
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4320/12
Therefore, the LCM is 360.
Example 2: Find the greatest number that divides 36 and 120 exactly.

Solution:

The greatest number that divides 36 and 120 exactly is their greatest common factor, i.e. GCF of 36 and 120.
⇒ Factors of 36 and 120:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 36 and 120 is 12.
Example 3: For two numbers, GCF = 12 and LCM = 360. If one number is 120, find the other number.

Solution:

Given: GCF (y, 120) = 12 and LCM (y, 120) = 360
∵ GCF × LCM = 120 × (y)
⇒ y = (GCF × LCM)/120
⇒ y = (12 × 360)/120
⇒ y = 36
Therefore, the other number is 36.

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FAQs on GCF of 36 and 120

What is the GCF of 36 and 120?

The GCF of 36 and 120 is 12. To calculate the greatest common factor (GCF) of 36 and 120, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 36 and 120, i.e., 12.

If the GCF of 120 and 36 is 12, Find its LCM.

GCF(120, 36) × LCM(120, 36) = 120 × 36
Since the GCF of 120 and 36 = 12
⇒ 12 × LCM(120, 36) = 4320
Therefore, LCM = 360
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How to Find the GCF of 36 and 120 by Long Division Method?

To find the GCF of 36, 120 using long division method, 120 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 36, 120?

The following equation can be used to express the relation between Least Common Multiple and GCF of 36 and 120, i.e. GCF × LCM = 36 × 120.

How to Find the GCF of 36 and 120 by Prime Factorization?

To find the GCF of 36 and 120, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 120. Hence, GCF(36, 120) = 2 × 2 × 3 = 12
☛ What are Prime Numbers?

What are the Methods to Find GCF of 36 and 120?

There are three commonly used methods to find the GCF of 36 and 120.

By Long Division
By Prime Factorization
By Listing Common Factors

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