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GCF of 64 and 96

GCF of 64 and 96 is the largest possible number that divides 64 and 96 exactly without any remainder. The factors of 64 and 96 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 respectively. There are 3 commonly used methods to find the GCF of 64 and 96 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 64 and 96
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 96?

Answer: GCF of 64 and 96 is 32.

Explanation:

The GCF of two non-zero integers, x(64) and y(96), is the greatest positive integer m(32) that divides both x(64) and y(96) without any remainder.

Methods to Find GCF of 64 and 96

The methods to find the GCF of 64 and 96 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 64 and 96 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

There are 6 common factors of 64 and 96, that are 32, 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 64 and 96 is 32.

GCF of 64 and 96 by Long Division

GCF of 64 and 96 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 96 (larger number) by 64 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (64) by the remainder (32).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (32) is the GCF of 64 and 96.

GCF of 64 and 96 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 96 and Y = 64

GCF(96, 64) = GCF(64, 96 mod 64) = GCF(64, 32)
GCF(64, 32) = GCF(32, 64 mod 32) = GCF(32, 0)
GCF(32, 0) = 32 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 64 and 96 is 32.

☛ Also Check:

GCF of 64 and 96 Examples

Example 1: The product of two numbers is 6144. If their GCF is 32, what is their LCM?

Solution:

Given: GCF = 32 and product of numbers = 6144
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6144/32
Therefore, the LCM is 192.
Example 2: For two numbers, GCF = 32 and LCM = 192. If one number is 96, find the other number.

Solution:

Given: GCF (y, 96) = 32 and LCM (y, 96) = 192
∵ GCF × LCM = 96 × (y)
⇒ y = (GCF × LCM)/96
⇒ y = (32 × 192)/96
⇒ y = 64
Therefore, the other number is 64.
Example 3: Find the greatest number that divides 64 and 96 exactly.

Solution:

The greatest number that divides 64 and 96 exactly is their greatest common factor, i.e. GCF of 64 and 96.
⇒ Factors of 64 and 96:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Therefore, the GCF of 64 and 96 is 32.

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FAQs on GCF of 64 and 96

What is the GCF of 64 and 96?

The GCF of 64 and 96 is 32. To calculate the GCF of 64 and 96, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 96 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96) and choose the greatest factor that exactly divides both 64 and 96, i.e., 32.

What are the Methods to Find GCF of 64 and 96?

There are three commonly used methods to find the GCF of 64 and 96.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 64 and 96 by Prime Factorization?

To find the GCF of 64 and 96, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 96 = 2 × 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2, 2 are common terms in the prime factorization of 64 and 96. Hence, GCF(64, 96) = 2 × 2 × 2 × 2 × 2 = 32
☛ Prime Number

If the GCF of 96 and 64 is 32, Find its LCM.

GCF(96, 64) × LCM(96, 64) = 96 × 64
Since the GCF of 96 and 64 = 32
⇒ 32 × LCM(96, 64) = 6144
Therefore, LCM = 192
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 64, 96?

The following equation can be used to express the relation between LCM and GCF of 64 and 96, i.e. GCF × LCM = 64 × 96.

How to Find the GCF of 64 and 96 by Long Division Method?

To find the GCF of 64, 96 using long division method, 96 is divided by 64. The corresponding divisor (32) when remainder equals 0 is taken as GCF.

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