NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks
Question 150

Question. 150

The HCF of two or more given numbers is the highest of their common ____.

Answer:

factors

Detailed Answer with Explanation:

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.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – Fill in the Blanks | Detailed Answers