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GCF of 9 and 36

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

1.	GCF of 9 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 36?

Answer: GCF of 9 and 36 is 9.

Explanation:

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

Methods to Find GCF of 9 and 36

The methods to find the GCF of 9 and 36 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 9 and 36 by Listing Common Factors

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

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

GCF of 9 and 36 by Long Division

GCF of 9 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 9 (smaller number).
Step 2: Since the remainder = 0, the divisor (9) is the GCF of 9 and 36.

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

GCF of 9 and 36 by Prime Factorization

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

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GCF of 9 and 36 Examples

Example 1: Find the greatest number that divides 9 and 36 exactly.

Solution:

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

Solution:

Given: GCF = 9 and product of numbers = 324
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 324/9
Therefore, the LCM is 36.
Example 3: For two numbers, GCF = 9 and LCM = 36. If one number is 9, find the other number.

Solution:

Given: GCF (y, 9) = 9 and LCM (y, 9) = 36
∵ GCF × LCM = 9 × (y)
⇒ y = (GCF × LCM)/9
⇒ y = (9 × 36)/9
⇒ y = 36
Therefore, the other number is 36.

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FAQs on GCF of 9 and 36

What is the GCF of 9 and 36?

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

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

GCF(36, 9) × LCM(36, 9) = 36 × 9
Since the GCF of 36 and 9 = 9
⇒ 9 × LCM(36, 9) = 324
Therefore, LCM = 36
☛ Greatest Common Factor Calculator

How to Find the GCF of 9 and 36 by Prime Factorization?

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

What are the Methods to Find GCF of 9 and 36?

There are three commonly used methods to find the GCF of 9 and 36.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 9 and 36 by Long Division Method?

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

What is the Relation Between LCM and GCF of 9, 36?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 9 and 36, i.e. GCF × LCM = 9 × 36.

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