The HCF of 2048 and 960 is 64. The highest common factor of 2048 and 960 is the value which divides the given two numbers evenly. The factors of 2048 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048,and the factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960. Students can better understand the prime factorisation, long division and listing common factors methods used in the calculation of HCF.
What is the HCF of 2048 and 960?
The answer to this question is 64. The HCF of 2048 and 960 determined using three various methods are provided in brief in this article. The HCF of 2048 and 960 is 64, which divides the given two numbers evenly.
Also read: Highest common factor
How to Find HCF of 2048 and 960?
The HCF of 2048 and 960 can be found using the methods below:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 2048 and 960 by Prime Factorisation Method
The prime factorisation of 2048 and 960 is:
2048 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
960 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5
The common prime factors of 2048 and 960 = 2, 2, 2, 2, 2, 2
Hence, HCF (2048, 960) = 2 × 2 × 2 × 2 × 2 × 2 = 64
HCF of 2048 and 960 by Long Division Method
We can divide (2048, 960) by the prime factors so that the HCF of 2048 and 960 can be found using the long division method. The divisor we get with zero as the remainder is the HCF of 2048 and 960.
No further division can be done.
Hence, HCF (2048, 960) = 64
HCF of 2048 and 960 by Listing Common Factors
The HCF of 2048 and 960 can be determined by listing the common factors as given below:
Factors of 2048: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048
Factors of 960: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
There are 7 common factors of 2048 and 960, and they are 1, 2, 4, 8, 16, 32 and 64.
Therefore, the highest common factor of 2048 and 960 is 64.
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Video Lesson on Properties of HCF and LCM
HCF of 2048 and 960 Solved Example
Question: Find the HCF of 2048 and 960 if the LCM is 30720.
Solution:
Given
LCM = 30720
We know that
HCF × LCM = 2048 × 960
HCF = (2048 × 960)/30720
HCF = 64
Hence, the HCF is 64.
Frequently Asked Questions on HCF of 2048 and 960
What is the HCF of 2048 and 960?
Calculate the HCF of 2048 and 960 using the long division method.
Write the methods used to find HCF of 2048 and 960.
If LCM = 30720 and HCF = 64 for two numbers, find the other number when one number is 960.
Consider y as the other number
Given LCM = 30720 and HCF = 64
HCF × LCM = 960 × y
y = (HCF × LCM)/ 960
y = (64 × 30720)/ 960
y = 2048
Therefore, the other number is 2048.
Show the relation between HCF and LCM of 2048 and 960.
The relation between HCF and LCM of 2048 and 960 is
HCF × LCM = 2048 × 960
HCF × LCM = 1966080
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