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GCF of 36 and 96

GCF of 36 and 96 is the largest possible number that divides 36 and 96 exactly without any remainder. The factors of 36 and 96 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 36 and 96 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 36 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 96?

Answer: GCF of 36 and 96 is 12.

Explanation:

The GCF of two non-zero integers, x(36) and y(96), is the greatest positive integer m(12) that divides both x(36) and y(96) without any remainder.

Methods to Find GCF of 36 and 96

The methods to find the GCF of 36 and 96 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 36 and 96 by Long Division

GCF of 36 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 96 (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 96.

GCF of 36 and 96 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 6 common factors of 36 and 96, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 96 is 12.

GCF of 36 and 96 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 = 96 and Y = 36

GCF(96, 36) = GCF(36, 96 mod 36) = GCF(36, 24)
GCF(36, 24) = GCF(24, 36 mod 24) = GCF(24, 12)
GCF(24, 12) = GCF(12, 24 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 96 is 12.

☛ Also Check:

GCF of 36 and 96 Examples

Example 1: Find the GCF of 36 and 96, if their LCM is 288.

Solution:

∵ LCM × GCF = 36 × 96
⇒ GCF(36, 96) = (36 × 96)/288 = 12
Therefore, the greatest common factor of 36 and 96 is 12.
Example 2: For two numbers, GCF = 12 and LCM = 288. If one number is 36, find the other number.

Solution:

Given: GCF (z, 36) = 12 and LCM (z, 36) = 288
∵ GCF × LCM = 36 × (z)
⇒ z = (GCF × LCM)/36
⇒ z = (12 × 288)/36
⇒ z = 96
Therefore, the other number is 96.
Example 3: Find the greatest number that divides 36 and 96 exactly.

Solution:

The greatest number that divides 36 and 96 exactly is their greatest common factor, i.e. GCF of 36 and 96.
⇒ Factors of 36 and 96:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 36 and 96 is 12.

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FAQs on GCF of 36 and 96

What is the GCF of 36 and 96?

The GCF of 36 and 96 is 12. To calculate the greatest common factor (GCF) of 36 and 96, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 36 and 96, i.e., 12.

What are the Methods to Find GCF of 36 and 96?

There are three commonly used methods to find the GCF of 36 and 96.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 96 and 36 is 12, Find its LCM.

GCF(96, 36) × LCM(96, 36) = 96 × 36
Since the GCF of 96 and 36 = 12
⇒ 12 × LCM(96, 36) = 3456
Therefore, LCM = 288
☛ Greatest Common Factor Calculator

How to Find the GCF of 36 and 96 by Prime Factorization?

To find the GCF of 36 and 96, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 96. Hence, GCF(36, 96) = 2 × 2 × 3 = 12
☛ Prime Number

What is the Relation Between LCM and GCF of 36, 96?

The following equation can be used to express the relation between LCM and GCF of 36 and 96, i.e. GCF × LCM = 36 × 96.

How to Find the GCF of 36 and 96 by Long Division Method?

To find the GCF of 36, 96 using long division method, 96 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

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