The HCF of 40, 60 and 75 is 5. The greatest number that divides 40, 60, and 75 exactly, leaving no remainder, is the HCF of these numbers. The listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 40, 60 and 75. The factors for 40, 60, and 75 are, (1, 2, 4, 5, 8, 10, 20, 40), (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), and (1, 3, 5, 15, 25, 75), respectively.
Also read: Highest common factor
What is the HCF of 40, 60 and 75?
The answer to this question is 5. This article shows the HCF of 40, 60 and 75 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 40, 60 and 75?
There are three methods to find the HCF of 40, 60 and 75:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 40, 60 and 75 by Prime Factorisation Method
The prime factorisation of 40, 60 and 75 is given by:
Prime factorisation of 40 = (2 × 2 × 2 × 5)
Prime factorisation of 60 = (2 × 2 × 3 × 5)
Prime factorisation of 75 = (3 × 5 × 5)
Hence, the HCF of 40, 60 and 75 is 5.
HCF (40, 60, 75) = 5
HCF of 40, 60 and 75 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing long division repeatedly is HCF of 40, 60 and 75.
No further division can be done.
Hence, HCF (40, 60, 75) = 5
HCF of 40, 60 and 75 by Listing the Factors
To calculate the HCF of 40, 60 and 75 by listing out the common factors, list the factors as shown below:
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 75: 1, 3, 5, 15, 25, 75
There are 2 common factors of 40, 60 and 75, that are 1 and 5. Therefore, the highest common factor of 40, 60 and 75 is 5
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HCF of 40, 60 and 75 Solved Example
Find the highest number that divides 40, 60, and 75 completely.
Solution:
The highest number that divides 40, 60, and 75 exactly is their highest common factor.
Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 75 = 1, 3, 5, 15, 25, 75
The HCF of 40, 60, and 75 is 5.
The highest number that divides 40, 60, and 75 is 5.
Frequently Asked Questions on HCF of 40, 60 and 75
What is the HCF of 40, 60 and 75?
How to Find the HCF of 40, 60 and 75 by Prime Factorisation?
⇒ Since 5 is the only common prime factor of 40, 60 and 75. Hence, HCF(40, 60, 75) = 5.
What are the Methods to Find HCF of 40, 60 and 75?
By Long Division
By Listing Common Factors
By Prime Factorisation
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