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GCF of 32 and 36

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

1.	GCF of 32 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 36?

Answer: GCF of 32 and 36 is 4.

Explanation:

The GCF of two non-zero integers, x(32) and y(36), is the greatest positive integer m(4) that divides both x(32) and y(36) without any remainder.

Methods to Find GCF of 32 and 36

The methods to find the GCF of 32 and 36 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 32 and 36 by Listing Common Factors

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

There are 3 common factors of 32 and 36, that are 1, 2, and 4. Therefore, the greatest common factor of 32 and 36 is 4.

GCF of 32 and 36 by Long Division

GCF of 32 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 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 32 and 36.

GCF of 32 and 36 by Prime Factorization

Prime factorization of 32 and 36 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 3 × 3) respectively. As visible, 32 and 36 have common prime factors. Hence, the GCF of 32 and 36 is 2 × 2 = 4.

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GCF of 32 and 36 Examples

Example 1: Find the greatest number that divides 32 and 36 exactly.

Solution:

The greatest number that divides 32 and 36 exactly is their greatest common factor, i.e. GCF of 32 and 36.
⇒ Factors of 32 and 36:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 32 and 36 is 4.
Example 2: Find the GCF of 32 and 36, if their LCM is 288.

Solution:

∵ LCM × GCF = 32 × 36
⇒ GCF(32, 36) = (32 × 36)/288 = 4
Therefore, the greatest common factor of 32 and 36 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 288. If one number is 36, find the other number.

Solution:

Given: GCF (y, 36) = 4 and LCM (y, 36) = 288
∵ GCF × LCM = 36 × (y)
⇒ y = (GCF × LCM)/36
⇒ y = (4 × 288)/36
⇒ y = 32
Therefore, the other number is 32.

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FAQs on GCF of 32 and 36

What is the GCF of 32 and 36?

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

What are the Methods to Find GCF of 32 and 36?

There are three commonly used methods to find the GCF of 32 and 36.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 32 and 36 by Long Division Method?

To find the GCF of 32, 36 using long division method, 36 is divided by 32. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

If the GCF of 36 and 32 is 4, Find its LCM.

GCF(36, 32) × LCM(36, 32) = 36 × 32
Since the GCF of 36 and 32 = 4
⇒ 4 × LCM(36, 32) = 1152
Therefore, LCM = 288
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What is the Relation Between LCM and GCF of 32, 36?

The following equation can be used to express the relation between Least Common Multiple and GCF of 32 and 36, i.e. GCF × LCM = 32 × 36.

How to Find the GCF of 32 and 36 by Prime Factorization?

To find the GCF of 32 and 36, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 32 and 36. Hence, GCF(32, 36) = 2 × 2 = 4
☛ What is a Prime Number?

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