Question

Determine o valor de n para que os números tenham:
a) 22 x 3" x 5 - 18 divisores
b) 23 x 32 x 7" - 36 divisores

"=n​

Answer 1

Explicação passo-a-passo:

a) $\sf (2+1)\cdot(n+1)\cdot(1+1)=18$

$\sf 3\cdot(n+1)\cdot2=18$

$\sf 6\cdot(n+1)=18$

$\sf n+1=\dfrac{18}{6}$

$\sf n+1=3$

$\sf n=3-1$

$\sf n=2$

b) $\sf (3+1)\cdot(2+1)\cdot(n+1)=36$

$\sf 4\cdot3\cdot(n+1)=36$

$\sf 12\cdot(n+1)=36$

$\sf n+1=\dfrac{36}{12}$

$\sf n+1=3$

$\sf n=3-1$

$\sf n=2$