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GCF of 64 and 32

GCF of 64 and 32 is the largest possible number that divides 64 and 32 exactly without any remainder. The factors of 64 and 32 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 64 and 32 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 64 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 32?

Answer: GCF of 64 and 32 is 32.

Explanation:

The GCF of two non-zero integers, x(64) and y(32), is the greatest positive integer m(32) that divides both x(64) and y(32) without any remainder.

Methods to Find GCF of 64 and 32

Let's look at the different methods for finding the GCF of 64 and 32.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 64 and 32 by Prime Factorization

Prime factorization of 64 and 32 is (2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 64 and 32 have common prime factors. Hence, the GCF of 64 and 32 is 2 × 2 × 2 × 2 × 2 = 32.

GCF of 64 and 32 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 32: 1, 2, 4, 8, 16, 32

There are 6 common factors of 64 and 32, that are 32, 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 64 and 32 is 32.

GCF of 64 and 32 by Long Division

GCF of 64 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 64 (larger number) by 32 (smaller number).
Step 2: Since the remainder = 0, the divisor (32) is the GCF of 64 and 32.

The corresponding divisor (32) is the GCF of 64 and 32.

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GCF of 64 and 32 Examples

Example 1: For two numbers, GCF = 32 and LCM = 64. If one number is 64, find the other number.

Solution:

Given: GCF (y, 64) = 32 and LCM (y, 64) = 64
∵ GCF × LCM = 64 × (y)
⇒ y = (GCF × LCM)/64
⇒ y = (32 × 64)/64
⇒ y = 32
Therefore, the other number is 32.
Example 2: Find the greatest number that divides 64 and 32 exactly.

Solution:

The greatest number that divides 64 and 32 exactly is their greatest common factor, i.e. GCF of 64 and 32.
⇒ Factors of 64 and 32:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 64 and 32 is 32.
Example 3: Find the GCF of 64 and 32, if their LCM is 64.

Solution:

∵ LCM × GCF = 64 × 32
⇒ GCF(64, 32) = (64 × 32)/64 = 32
Therefore, the greatest common factor of 64 and 32 is 32.

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FAQs on GCF of 64 and 32

What is the GCF of 64 and 32?

The GCF of 64 and 32 is 32. To calculate the greatest common factor of 64 and 32, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 64 and 32, i.e., 32.

If the GCF of 32 and 64 is 32, Find its LCM.

GCF(32, 64) × LCM(32, 64) = 32 × 64
Since the GCF of 32 and 64 = 32
⇒ 32 × LCM(32, 64) = 2048
Therefore, LCM = 64
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 64, 32?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 64 and 32, i.e. GCF × LCM = 64 × 32.

How to Find the GCF of 64 and 32 by Long Division Method?

To find the GCF of 64, 32 using long division method, 64 is divided by 32. The corresponding divisor (32) when remainder equals 0 is taken as GCF.

How to Find the GCF of 64 and 32 by Prime Factorization?

To find the GCF of 64 and 32, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2, 2, 2 are common terms in the prime factorization of 64 and 32. Hence, GCF(64, 32) = 2 × 2 × 2 × 2 × 2 = 32
☛ What are Prime Numbers?

What are the Methods to Find GCF of 64 and 32?

There are three commonly used methods to find the GCF of 64 and 32.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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