Question

Find the number of divisors and sum of divisors of the number $1400$. Also find the number of ways of putting $1400$ as a product of two factors.

Answer 1

$1400=2^3\times 5^2\times 7$

Number of divisors $=(3+1)\times (2+1)\times (1+1)=24$

Sum of divisors $=\frac{2^4-1}{2-1}\times \frac{5^3-1}{5-1}\times \frac{7^2-1}{7-1}=3720$