The HCF of 408 and 1032 is 24. The largest integer, which evenly divides the numbers 408 and 1032, gives the HCF. The subject experts use simple steps to improve the conceptual knowledge of students. The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408, and the factors of 1032 are 1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032. You can find the HCF of given numbers using methods, prime factorisation, long division and listing common factors.
What is the HCF of 408 and 1032?
The answer to this question is 24. The steps used to find the HCF of 408 and 1032 using different methods are provided in this article for a good hold on the concepts. The HCF of 408 and 1032 is 24, divides 408 and 1032 evenly.
Also read: Highest common factor
How to Find HCF of 408 and 1032?
There are three methods to find the HCF of 408 and 1032
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 408 and 1032 by Prime Factorisation Method
The prime factorisation of 408 and 1032 is given by:
408 = 2 × 2 × 2 × 3 × 17
1032 = 2 × 2 × 2 × 3 × 43
Common prime factors of 408 and 1032 = 2, 2, 2, 3
Therefore, HCF (408, 1032) = 2 × 2 × 2 × 3 = 24
HCF of 408 and 1032 by Long Division Method
We should divide 408 and 1032 by their factors to determine the HCF with the help of the division method. The HCF of 408 and 1032 is the divisor obtained when the remainder is zero after repeated long division.
No further division can be done.
Hence, HCF (408, 1032) = 24
HCF of 408 and 1032 by Listing Common Factors
To calculate the HCF of 408 and 1032, the common factors have to be listed as given below:
Factors of 408: 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
Factors of 1032: 1, 2, 3, 4, 6, 8, 12, 24, 43, 86, 129, 172, 258, 344, 516, 1032
There are 8 common factors of 408 and 1032, and they are 1, 2, 3, 4, 6, 8, 12 and 24.
Therefore, the highest common factor of 408 and 1032 is 24.
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Video Lesson on Properties of HCF and LCM
HCF of 408 and 1032 Solved Example
Question: If HCF = 24 and product of two numbers = 421056, find the LCM.
Solution:
Given
HCF = 24
Product = 421056
We know that
HCF × LCM = Product
LCM = Product/HCF
LCM = 421056/24
LCM = 17544
Hence, the LCM is 17544.
Frequently Asked Questions on HCF of 408 and 1032
What is the HCF of 408 and 1032?
How can we find the HCF of 408 and 1032 using the long division method?
Which methods can be used to find the HCF of 408 and 1032?
If LCM = 17544 and HCF = 24 for two numbers, determine the other number when one number is 1032.
Consider y as the other number
Given LCM = 17544 and HCF = 24
HCF × LCM = 1032 × y
y = (HCF × LCM)/ 1032
y = (24 × 17544)/ 1032
y = 408
Therefore, the other number is 408.
Show the relation between HCF and LCM of 408 and 1032.
The relation between HCF and LCM of 408 and 1032 is
HCF × LCM = 408 × 1032
HCF × LCM = 421056
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