NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks

Question 150

Idea: HCF means Highest Common Factor. It is the biggest number that divides each of the given numbers exactly (with no remainder).

1. Understand “factor”
   

   A factor of a number is a whole number that divides it exactly.

   Example: Factors of \(12\) are
   \(1,\ 2,\ 3,\ 4,\ 6,\ 12\).

2. Understand “common factors”
   

   These are the factors that are present in all the given numbers.

   Example: For \(12\) and \(18\):

   Factors of \(12\): \(1,\ 2,\ 3,\ 4,\ 6,\ 12\)

   Factors of \(18\): \(1,\ 2,\ 3,\ 6,\ 9,\ 18\)

   Common factors: \(1,\ 2,\ 3,\ 6\)

3. Pick the highest common factor
   

   From \(1,\ 2,\ 3,\ 6\), the highest is \(6\).

   So, \(\text{HCF}(12,18)=6\).

Therefore: The HCF of two or more numbers is the highest of their common factors.

Tip: You can also find HCF by prime factorization and then taking the common primes with the smallest powers.