Question

Find the total number of positive divisors of $8640$ including the trivial divisor.

• A. $56$
• B. $57$
• C. $58$
• D. $59$

Answer 1

The correct option is B $57$

$8640=2^6{3}^{3}5$
Hence, the number of non-trivial divisors of $8640$ are $=(6+1)(3+1)(1+1)=7\times 4\times 2=56$
Hence, the total number of divisors (including the trivial divisor $1$) will be $=56+1=57$