Question

Si N = 32^2x X 5^x , tiene 15 divisores, hallar N
PD: ^ SIGNIFICA POTENCIA, porsiacaso.

Answer 1

$N=2^{2x}\times 5^x\\ \\ \text{N\'umero de divisores:}\\ \\ (2x+1)(x+1)=15\\ 2x^2+3x+1=15\\ 2x^2+3x-14=0\\ (x-2)(2x+7)=0\\ \boxed{x=2}\\ \\ \therefore \boxed{\boxed{N=2^4\times 5^2=400}}$