Question

# Find the HCF of $15$,$25$and $30$.

Hint: Try to find individual factors.

HCF is the Highest common factor.
HCF for two or more numbers is the largest number that divides each one of them without leaving a remainder.
Given the numbers $15$,$25$and $30$.
First, we need to find the individual factors of each number.
Factors of 15, ${S_1} = \left\{ {1,3,5,15} \right\}$
Factors of 25, ${S_2} = \left\{ {1,5,25} \right\}$
Factors of 30, ${S_3} = \left\{ {1,3,5,6,10,15} \right\}$
Common factors of $15$,$25$and $30$ are
${S_1} \cap {S_2} \cap {S_3} = \left\{ {1,5} \right\}$
The largest number in the above set is $5$.
Hence the HCF of $15$,$25$and $30$ is $5$.
Note: HCF is also known as the Greatest Common Measure (GCM) and Greatest Common Divisor (GCD). HCF is always less than equal to the smallest number involved. Two or more prime numbers have HCF $= 1$.
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