How to Find the HCF of 10 and 12 - Detailed Methods Explained

Last Updated on Jun 13, 2024
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The Highest Common Factor (HCF) of 10 and 12 is 2 . Both 10 and 12 can be divided by this number without any remainder. The factors of 10 include 1, 2, 5, 10 while the factors of 12 are 1, 2, 3, 4, 6, 12. There are several methods to determine the HCF including prime factorisation, long division and listing common factors. This article is designed to help students gain a strong understanding of the basic principles of Mathematics.

Also read: Understanding the Highest Common Factor

How is the HCF of 10 and 12 determined?

The HCF of 10 and 12 is 2. There are three common methods that can be used to calculate the HCF of these numbers.

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Techniques to Calculate the HCF of 10 and 12

The following methods can be used to find the HCF of 10 and 12:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

Using Prime Factorisation to Find the HCF of 10 and 12

The prime factorisation of 10 and 12 is:

10 = 2 × 5

12 = 2 × 2 × 3

The common prime factors of 10 and 12 = 2

Therefore, HCF (10, 12) = 2

Using Long Division to Find the HCF of 10 and 12

If we divide 10 and 12 by their factors, we can find the HCF. The divisor in the long division when the remainder is zero will be the HCF.

Further division is not possible.

Thus, HCF (10, 12) = 2

Using Listing Common Factors to Find the HCF of 10 and 12

Here's how you can find the HCF of 10 and 12 by listing common factors:

Factors of 10: 1, 2, 5, 10

Factors of 12: 1, 2, 3, 4, 6, 12

The common factors of 10 and 12 are 1 and 2.

Thus, the highest common factor of 10 and 12 is 2.

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Example of HCF of 10 and 12

Question: Given that the LCM is 60, what is the HCF of 10 and 12?

Solution:

Given

LCM = 60

HCF × LCM = 10 × 12

HCF = (10 × 12)/ 60

HCF = 2

Hence, the HCF is 2.

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Frequently Asked Questions

The HCF of 10 and 12 is 2.

10 = 2 × 5, 12 = 2 × 2 × 3. Hence, the HCF is 2.

The methods which can be used to find the HCF of 10 and 12 are Long Division, Listing Common Factors and Prime Factorisation.

Given HCF = 2 and Product = 120, HCF × LCM = Product. Therefore, LCM = 120/2, which equals 60.

The relation between HCF and LCM of 10 and 12 is HCF × LCM = 10 × 12, which equals 120.

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