Question

If $a,b,c$ are distinct positive prime integers such that $a^2{b}^3{c}^4=49392,$ find the values of $a,b$ and $c.$

Answer 1

By prime factorization, we can rewrite $49392,$

$49392=2\times 2\times 2\times 2\times 3\times 3\times 7\times 7\times 7$

$49392=2^4\times 3^2\times 7^3$

On comparing the factorized form with $a^2{b}^3{c}^4$ we get,

$a^2{b}^3{c}^4=2^4\times 3^2\times 7^3$

If,

$a=3,b=7$ and $c=2$