The HCF of 1152 and 1664 is 128. The highest possible number that divides 1152 and 1664 perfectly without any residual is the HCF of 1152 and 1664. The factors of 1152 and 1664 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152 and 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664, respectively. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 1152 and 1664.
Also read: Highest common factor
What is the HCF of 1152 and 1664?
The answer to this question is 128. This article shows the HCF of 1152 and 1664 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 1152 and 1664?
There are three methods to find the HCF of 1152 and 1664:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 1152 and 1664 by Prime Factorisation Method
The prime factorisation of 1152 and 1664 is given by:
Prime factorisation of 1152 = (2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3)
Prime factorisation of 1664 = (2 × 2 × 2 × 2 × 2 × 2 × 2 × 13)
Hence, the HCF of 1152 and 1664 is 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128.
HCF (1152, 1664) = 128
HCF of 1152 and 1664 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is the HCF of 1152 and 1664.
No further division can be done.
Hence, HCF (1152, 1664) = 128
HCF of 1152 and 1664 by Listing Common Factors
To calculate the HCF of 1152 and 1664 by listing out the common factors, list the factors as shown below:
Factors of 1152: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 288, 384, 576, 1152
Factors of 1664: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832, 1664
There are 8 common factors of 1152 and 1664, and they are 1, 2, 4, 8, 16, 32, 64, and 128. Therefore, the highest common factor of 1152 and 1664 is 128.
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HCF of 1152 and 1664 Solved Example
Question: For two numbers, HCF = 128 and LCM = 14976. If one number is 1664, find the other number.
Solution:
Given: HCF (z, 1664) = 128 and LCM (z, 1664) = 14976
∵ HCF × LCM = 1664 × (z)
⇒ z = (HCF × LCM)/1664
⇒ z = (128 × 14976)/1664
⇒ z = 1916928/1664 = 1152
Therefore, the other number is 1152.
Frequently Asked Questions on HCF of 1152 and 1664
What is the HCF of 1152 and 1664?
How to find the HCF of 1152 and 1664 by long division method?
What are the methods to find HCF of 1152 and 1664?
By Long Division
By Listing Common Factors
By Prime Factorisation
How to find the HCF of 1152 and 1664 by prime factorisation?
⇒ Since 2, 2, 2, 2, 2, 2, 2 are common numbers in the prime factorisation of 1152 and 1664, HCF(1152, 1664) = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128
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