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
The HCF of 10 and 12 is 2. There are three common methods that can be used to calculate the HCF of these numbers.
The following methods can be used 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
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
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.
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.
What is the HCF of 10 and 12?
The HCF of 10 and 12 is 2.
Using the prime factorisation method, find the HCF of 10 and 12.
10 = 2 × 5, 12 = 2 × 2 × 3. Hence, the HCF is 2.
What methods can be used to find HCF of 10 and 12?
The methods which can be used to find the HCF of 10 and 12 are Long Division, Listing Common Factors and Prime Factorisation.
Find the LCM if the HCF is 2 and the product of two numbers is 120.
Given HCF = 2 and Product = 120, HCF × LCM = Product. Therefore, LCM = 120/2, which equals 60.
Mention the relation between HCF and LCM of 10 and 12.
The relation between HCF and LCM of 10 and 12 is HCF × LCM = 10 × 12, which equals 120.