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GCF of 36 and 54

GCF of 36 and 54 is the largest possible number that divides 36 and 54 exactly without any remainder. The factors of 36 and 54 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the GCF of 36 and 54 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 36 and 54
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 54?

Answer: GCF of 36 and 54 is 18.

Explanation:

The GCF of two non-zero integers, x(36) and y(54), is the greatest positive integer m(18) that divides both x(36) and y(54) without any remainder.

Methods to Find GCF of 36 and 54

Let's look at the different methods for finding the GCF of 36 and 54.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 36 and 54 by Long Division

GCF of 36 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 54 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (18) is the GCF of 36 and 54.

GCF of 36 and 54 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

There are 6 common factors of 36 and 54, that are 1, 2, 3, 6, 9, and 18. Therefore, the greatest common factor of 36 and 54 is 18.

GCF of 36 and 54 by Prime Factorization

Prime factorization of 36 and 54 is (2 × 2 × 3 × 3) and (2 × 3 × 3 × 3) respectively. As visible, 36 and 54 have common prime factors. Hence, the GCF of 36 and 54 is 2 × 3 × 3 = 18.

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GCF of 36 and 54 Examples

Example 1: Find the GCF of 36 and 54, if their LCM is 108.

Solution:

∵ LCM × GCF = 36 × 54
⇒ GCF(36, 54) = (36 × 54)/108 = 18
Therefore, the greatest common factor of 36 and 54 is 18.
Example 2: Find the greatest number that divides 36 and 54 exactly.

Solution:

The greatest number that divides 36 and 54 exactly is their greatest common factor, i.e. GCF of 36 and 54.
⇒ Factors of 36 and 54:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Therefore, the GCF of 36 and 54 is 18.
Example 3: For two numbers, GCF = 18 and LCM = 108. If one number is 36, find the other number.

Solution:

Given: GCF (y, 36) = 18 and LCM (y, 36) = 108
∵ GCF × LCM = 36 × (y)
⇒ y = (GCF × LCM)/36
⇒ y = (18 × 108)/36
⇒ y = 54
Therefore, the other number is 54.

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FAQs on GCF of 36 and 54

What is the GCF of 36 and 54?

The GCF of 36 and 54 is 18. To calculate the greatest common factor (GCF) of 36 and 54, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the greatest factor that exactly divides both 36 and 54, i.e., 18.

How to Find the GCF of 36 and 54 by Prime Factorization?

To find the GCF of 36 and 54, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 36 and 54. Hence, GCF(36, 54) = 2 × 3 × 3 = 18
☛ Prime Numbers

What are the Methods to Find GCF of 36 and 54?

There are three commonly used methods to find the GCF of 36 and 54.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 36, 54?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 36 and 54, i.e. GCF × LCM = 36 × 54.

How to Find the GCF of 36 and 54 by Long Division Method?

To find the GCF of 36, 54 using long division method, 54 is divided by 36. The corresponding divisor (18) when remainder equals 0 is taken as GCF.

If the GCF of 54 and 36 is 18, Find its LCM.

GCF(54, 36) × LCM(54, 36) = 54 × 36
Since the GCF of 54 and 36 = 18
⇒ 18 × LCM(54, 36) = 1944
Therefore, LCM = 108
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