Question

the total numbers of factors (excluding 1) of 2160

Answer 1

$2160 = {2}^{4} \times {3}^{3} \times 5$

Number of factors = Product of highest power of each prime factors with an increment of 1

Therefore , number of factors of 2160 =

$(4 + 1)(3 + 1)(1 + 1) = 5 \times 4 \times 2$

Hence , there are 40 factors