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GCF of 36 and 81

GCF of 36 and 81 is the largest possible number that divides 36 and 81 exactly without any remainder. The factors of 36 and 81 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 36 and 81 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 36 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 81?

Answer: GCF of 36 and 81 is 9.

Explanation:

The GCF of two non-zero integers, x(36) and y(81), is the greatest positive integer m(9) that divides both x(36) and y(81) without any remainder.

Methods to Find GCF of 36 and 81

The methods to find the GCF of 36 and 81 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 36 and 81 by Long Division

GCF of 36 and 81 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 81 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 36 and 81.

GCF of 36 and 81 by Prime Factorization

Prime factorization of 36 and 81 is (2 × 2 × 3 × 3) and (3 × 3 × 3 × 3) respectively. As visible, 36 and 81 have common prime factors. Hence, the GCF of 36 and 81 is 3 × 3 = 9.

GCF of 36 and 81 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 81: 1, 3, 9, 27, 81

There are 3 common factors of 36 and 81, that are 1, 3, and 9. Therefore, the greatest common factor of 36 and 81 is 9.

☛ Also Check:

GCF of 36 and 81 Examples

Example 1: Find the greatest number that divides 36 and 81 exactly.

Solution:

The greatest number that divides 36 and 81 exactly is their greatest common factor, i.e. GCF of 36 and 81.
⇒ Factors of 36 and 81:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 36 and 81 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 324. If one number is 81, find the other number.

Solution:

Given: GCF (x, 81) = 9 and LCM (x, 81) = 324
∵ GCF × LCM = 81 × (x)
⇒ x = (GCF × LCM)/81
⇒ x = (9 × 324)/81
⇒ x = 36
Therefore, the other number is 36.
Example 3: Find the GCF of 36 and 81, if their LCM is 324.

Solution:

∵ LCM × GCF = 36 × 81
⇒ GCF(36, 81) = (36 × 81)/324 = 9
Therefore, the greatest common factor of 36 and 81 is 9.

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FAQs on GCF of 36 and 81

What is the GCF of 36 and 81?

The GCF of 36 and 81 is 9. To calculate the greatest common factor (GCF) of 36 and 81, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 36 and 81, i.e., 9.

How to Find the GCF of 36 and 81 by Long Division Method?

To find the GCF of 36, 81 using long division method, 81 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 36, 81?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 36 and 81, i.e. GCF × LCM = 36 × 81.

How to Find the GCF of 36 and 81 by Prime Factorization?

To find the GCF of 36 and 81, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 36 and 81. Hence, GCF(36, 81) = 3 × 3 = 9
☛ Prime Numbers

If the GCF of 81 and 36 is 9, Find its LCM.

GCF(81, 36) × LCM(81, 36) = 81 × 36
Since the GCF of 81 and 36 = 9
⇒ 9 × LCM(81, 36) = 2916
Therefore, LCM = 324
☛ GCF Calculator

What are the Methods to Find GCF of 36 and 81?

There are three commonly used methods to find the GCF of 36 and 81.

By Prime Factorization
By Listing Common Factors
By Long Division

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