+1 vote
18 views

The number of ways in which the number $1440$ can be expressed as a product of two factors is equal to

1. $18$
2. $720$
3. $360$
4. $36$

recategorized | 18 views

Option A) 18 is correct

$1440=2^5*3^2*5^1$

No of factors of $1440$= $(5+1)(2+1)(1+1)$=$36$

1440 is not a perfect square so no of ways it can be written as product of two factors = $36/2=18$

If n is not a perfect square then no of ways it can be written as product of factors= (# of factors of n)/2

If n is a perfect square then no of ways it can be written as product of factors = (# of factors of n -1)/2

by Boss (15.6k points)