Question

Find the H.C.F. of $25,65$ by prime factorization method .

Answer 1

Finding the H..C.F. by prime factorization :

Highest common factor ( H.C.F. ) of two natural numbers is the largest common factor ( or divisor ) of the given numbers.

Prime factorization of given numbers are :

$$\begin{gathered} 25=5\times 5 \\ 65=5\times 13 \end{gathered}$$

Here, notice that $5$ occurs as a common prime factor at least once in the prime factors of the given numbers

$\mathrm{HCF}(25,65)=5$

Hence , H.C.F. of $25,65$ is $5$