Question

Find the H.C.F. of $105,140,175$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 numbe

Prime Factorization of given numbers are :

$$\begin{gathered} 105=3\times 5\times 7 \\ 140=2\times 2\times 5\times 7 \\ 175=5\times 5\times 7 \end{gathered}$$

Here, $5$ occurs as a common prime factor at least once and $7$ occurs also at least once in the prime factors of given numbers.

$\begin{array}{rcl}\mathrm{HCF}(105,140,175)& =& 5\times 7\\ & =& 35\end{array}$.

Hence , H.C.F. of $105,140,175$ is $35$