Question

If $49392=a^4{b}^2{c}^3$, find the values of a, b and c, where a, b and c are different positive primes.

Answer 1

First find out the prime factorisation of 49392.

$\begin{array}{cc}2& 49392\\ 2& 24696\\ 2& 12348\\ 2& 6174\\ 3& 3087\\ 3& 1029\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

It can be observed that 49392 can be written as $2^4\times 3^2\times 7^3$, where 2, 3 and 7 are positive primes.
$$\begin{gathered} \therefore 49392=2^4{3}^2{7}^3=a^4{b}^2{c}^3 \\ \Rightarrow a=2,b=3,c=7 \end{gathered}$$