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GCF of 120 and 36

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

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

What is GCF of 120 and 36?

Answer: GCF of 120 and 36 is 12.

Explanation:

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

Methods to Find GCF of 120 and 36

Let's look at the different methods for finding the GCF of 120 and 36.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 120 and 36 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 120 and 36 is 12.

GCF of 120 and 36 by Listing Common Factors

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 6 common factors of 120 and 36, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 120 and 36 is 12.

GCF of 120 and 36 by Long Division

GCF of 120 and 36 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 120 and 36.

☛ Also Check:

GCF of 120 and 36 Examples

Example 1: Find the GCF of 120 and 36, if their LCM is 360.

Solution:

∵ LCM × GCF = 120 × 36
⇒ GCF(120, 36) = (120 × 36)/360 = 12
Therefore, the greatest common factor of 120 and 36 is 12.
Example 2: For two numbers, GCF = 12 and LCM = 360. If one number is 120, find the other number.

Solution:

Given: GCF (z, 120) = 12 and LCM (z, 120) = 360
∵ GCF × LCM = 120 × (z)
⇒ z = (GCF × LCM)/120
⇒ z = (12 × 360)/120
⇒ z = 36
Therefore, the other number is 36.
Example 3: Find the greatest number that divides 120 and 36 exactly.

Solution:

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

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FAQs on GCF of 120 and 36

What is the GCF of 120 and 36?

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

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

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

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

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

By Euclidean Algorithm
By Prime Factorization
By Long Division

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

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

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

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

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

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