Question

1.Cati divizori are nr 30000?

Answer 1

30.000 = 2⁴ × 3 × 5⁴

NrD = (4 + 1)(1 + 1)(4 + 1) = 5 × 2 × 5 = 50 de divizori

Answer 2

30000 = 3 × (2 × 5) ^ 4 = 3 × 2 × 5 × 2 × 5 × 2 × 5

Nr de divizori = ${2}^{nr \: de \: factori \: primi} - 1 - nr \: de \: factori \: care \: se \: repeta = {2}^{7} - 1 - 4 = 128 - 1 - 4 = 123$divizori
(2 se repeta de 2 ori dupa ce a aparut prima data si 5 la fel)