The HCF of two or more given numbers is the highest of their common ____.
factors
Idea: HCF means Highest Common Factor. It is the biggest number that divides each of the given numbers exactly (with no remainder).
A factor of a number is a whole number that divides it exactly.
Example: Factors of \(12\) are
\(1,\ 2,\ 3,\ 4,\ 6,\ 12\).
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: \(1,\ 2,\ 3,\ 6\)
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.