HCF of 4 and 10

The HCF of 4 and 10 is 2. HCF is the greatest integer that can divide 4 and 10, evenly, and that number is 2. HCF stands for Highest Common Factor. 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 4 and 10, the common factors are 1 and 2. Since 2 is the highest among the given factors, HCF would be 2, for 4 and 10. You can refer to GCF for more details.

What is the HCF of 4 and 10?

The Highest Common Factor, also known as the Greatest Common Factor of 4 and 10, is 2. 

How to Find HCF of 4 and 10?

There are three methods to find the HCF of 4 and 10:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 4 and 10 by Prime Factorisation Method

In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 4 and 10 can be expressed as:

4 = 2 × 2 

10 = 2 × 5 

The common prime factor is 2. 

Therefore HCF (4, 10) = 2

HCF of 4 and 10 by Long Division Method

In the long division method, the following 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 4 and 10 by long division method is:

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Therefore, HCF (4, 10) = 2

HCF of 4 and 10 by Listing Common Factors

By listing common factors of given numbers, we can identify the Highest/Greatest/Biggest Common Factor, which is the HCF. Below is the list of factors for 4 and 10:

Factors of 4: 1, 2, and 4

Factors of 10: 1, 2, 5, and 10

Therefore, HCF (4, 10) = 2

Related Articles

Video Lesson on Properties of HCF and LCM

Solved Examples

1. Find the greatest number that divides 4 and 10.

Solution: The greatest number that divides both 4 and 10 is nothing but the GCF, which is 2.

2. What is the HCF of 11 and 21?

Solution: The HCF of 11 and 21 is 1.

Frequently Asked Questions on HCF of 4 and 10

Q1

What is the HCF of 4 and 10?

The HCF of 4 and 10 is 2.
Q2

What is the HCF of 2, 4 and 10?

The HCF of 2, 4 and 10 is 2.
Q3

What is the second HCF of 4 and 10?

The second HCF of 4 and 10 is 1.
Q4

Is the HCF of 4 and 10 the same as the LCM of 4 and 10?

No. The Highest Common Factor (HCF) of 4 and 10 is 2, and the Least Common Multiple (LCM) of 4 and 10 is 20.
Q5

What are the common factors of 4 and 10?

1 and 2 are the common factors of 4 and 10.

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