Question

Find the H.C.F of $28,36$ 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 :

$$\begin{gathered} 28=2\times 2\times 7 \\ 36=2\times 2\times 3\times 3 \end{gathered}$$

Notice that 2 occurs as a common prime factor two times in the prime factors of given numbers. Therefore,

$\begin{array}{rcl}\mathrm{HCF}(28,36)& =& 2\times 2\\ & =& 4\end{array}$

Hence, H.C.F. of $28,36$is $4$.