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HCF of 64 and 96

HCF 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 HCF of 64 and 96 - Euclidean algorithm, long division, and prime factorization.

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

What is HCF of 64 and 96?

Answer: HCF of 64 and 96 is 32.

Explanation:

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

Methods to Find HCF of 64 and 96

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

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 64 and 96 by Long Division

HCF 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 HCF of 64 and 96.

HCF of 64 and 96 by Prime Factorization

Prime factorization of 64 and 96 is (2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2 × 3) respectively. As visible, 64 and 96 have common prime factors. Hence, the HCF of 64 and 96 is 2 × 2 × 2 × 2 × 2 = 32.

HCF of 64 and 96 by Euclidean Algorithm

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

Here X = 96 and Y = 64

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

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

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HCF of 64 and 96 Examples

Example 1: Find the highest number that divides 64 and 96 exactly.

Solution:

The highest number that divides 64 and 96 exactly is their highest common factor, i.e. HCF 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 HCF of 64 and 96 is 32.
Example 2: For two numbers, HCF = 32 and LCM = 192. If one number is 96, find the other number.

Solution:

Given: HCF (z, 96) = 32 and LCM (z, 96) = 192
∵ HCF × LCM = 96 × (z)
⇒ z = (HCF × LCM)/96
⇒ z = (32 × 192)/96
⇒ z = 64
Therefore, the other number is 64.
Example 3: The product of two numbers is 6144. If their HCF is 32, what is their LCM?

Solution:

Given: HCF = 32 and product of numbers = 6144
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 6144/32
Therefore, the LCM is 192.

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FAQs on HCF of 64 and 96

What is the HCF of 64 and 96?

The HCF of 64 and 96 is 32. To calculate the Highest common factor (HCF) 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 highest factor that exactly divides both 64 and 96, i.e., 32.

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

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

By Long Division
By Prime Factorization
By Listing Common Factors

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

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

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

HCF(96, 64) × LCM(96, 64) = 96 × 64
Since the HCF of 96 and 64 = 32
⇒ 32 × LCM(96, 64) = 6144
Therefore, LCM = 192
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How to Find the HCF of 64 and 96 by Prime Factorization?

To find the HCF 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, HCF(64, 96) = 2 × 2 × 2 × 2 × 2 = 32
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How to Find the HCF of 64 and 96 by Long Division Method?

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

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