Question

Find the H.C.F. of $54,72,90$ 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 :

$$\begin{gathered} 54=2\times 3\times 3\times 3 \\ 72=2\times 2\times 2\times 3\times 3 \\ 90=2\times 3\times 3\times 5 \end{gathered}$$

Here, notice that $2$ occurs as a common prime factor at least once and $3$ for two times in the prime factors of three given numbers

$\begin{array}{rcl}\mathrm{HCF}(54,72,90)& =& 2\times 3\times 3\\ & =& 18\end{array}$.

Hence, H.C.F. of $54,72,90$ is $18$