HCF of 60 and 75

The HCF of 60 and 75 is 15. HCF of 60 and 75 is the greatest integer that can divide both numbers evenly, and that number is 15. HCF stands for Highest Common Factor, and it is also known as GCF, Greatest Common Factor or GCD, Greatest Common Divisor. For a given set of numbers, there would be multiple common factors, and the highest among the common factors is known as the HCF. For 60 and 75, the common factors are 1, 3, 5 and 15. Since 15 is the highest among the given factors, HCF would be 15 for 60 and 75. You can refer to GCF for more details.

What is the HCF of 60 and 75?

The Highest Common Factor, also known as the Greatest Common Factor, of 60 and 75 is 15. 

How to Find HCF of 60 and 75?

There are three methods to find the HCF of 60 and 75:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 60 and 75 by Prime Factorisation Method

In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 60 and 75 can be expressed as:

60 = 2 × 2 × 3 × 5 

75 = 3 × 5 × 5

Common prime factors of 60 and 75 are 3 and 5.

Therefore, HCF (60, 75) = 3 × 5 = 15.

HCF of 60 and 75 by Long Division Method

In the long division method, the below steps are followed.

  1. From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
  2. In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor. 
  3. The above step is followed until the remainder is zero. 
  4. The last divisor would be the HCF.

The HCF of 60 and 75 by long division method is:

HCF 31

Therefore, HCF (60, 75) = 15

HCF of 60 and 75 by Listing Common Factors

By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 60 and 75:

Factors of 60:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors of 75:

 1, 3, 5, 15, 25, 75

Therefore, HCF (60, 75) = 15

Related Articles

Video Lesson on Properties of HCF and LCM

Solved Examples

1. Find the second greatest number that divides 60 and 75 evenly.

The second greatest number that divides both 60 and 75 evenly is nothing but the second greatest common factor, which is 5.

2. What is the GCF of 15 and 150?

The GCF of 15 and 150 is 15.

Frequently Asked Questions on HCF of 60 and 75

Q1

What is the HCF of 60 and 75?

The HCF of 60 and 75 is 15.
Q2

What is the HCF of 15, 60 and 75?

The HCF of 15, 60 and 75 is 15.
Q3

Is the HCF of 60 and 75 the same as the LCM of 60 and 75?

No, the Highest Common Factor of 60 and 75 is 15 and the Least Common Multiple of 60 and 75 is 300.
Q4

What are the common prime factors of 60 and 75?

The common prime factors of 60 and 75 are 3 and 5.
Q5

What are the three common multiples of 60 and 75?

The three common multiples of 60 and 75 are 300, 600 and 900.

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