The HCF of 64 and 96 is 32. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 64 and 96. The greatest number that divides 64 and 96 perfectly without leaving a residue is the HCF of 64 and 96. 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.
Also read: Highest common factor
What is the HCF of 64 and 96?
The answer to this question is 32. This article shows how to find the HCF of 64 and 96 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.
How to Find HCF of 64 and 96?
There are three methods to find the HCF of 64 and 96:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 64 and 96 by Prime Factorisation Method
The prime factorisation of 64 and 96 is given by:
Prime factorisation of 64 = (2 × 2 × 2 × 2 × 2 × 2)
Prime factorisation of 96 = (2 × 2 × 2 × 2 × 2 × 3)
Common prime factors of 64 and 96 are 2, 2, 2, 2 and 2.
Hence, the HCF of 64 and 96 is 2 × 2 × 2 × 2 × 2 = 32.
HCF (64, 96) = 32
HCF of 64 and 96 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is the HCF of 64 and 96.
No further division can be done.
Hence, HCF (64, 96) = 32
HCF of 64 and 96 by Listing Common Factors
To calculate the HCF of 64 and 96 by listing out the common factors, list the factors as shown below:
Factors of 64: 1, 2, 4, 8, 16, 32 and 64
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96.
There are 4 common factors of 64 and 96, and they are 1, 2, 4, 8, 12, 16 and 32. Therefore, the highest common factor of 64 and 96 is 32.
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HCF of 64 and 96 Solved Example
Question: 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.
Frequently Asked Questions on HCF of 64 and 96
What is the HCF of 64 and 96?
What is the relation between LCM and HCF of 64, 96?
What are the methods to find HCF of 64 and 96?
By Long Division
By Listing Common Factors
By Prime Factorisation
If the HCF of 96 and 64 is 32, Find its LCM.
Since the HCF of 96 and 64 = 32
⇒ 32 × LCM(96, 64) = 6144
LCM(96, 64) = 6144/32 = 192
Therefore, LCM = 192
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