why only perfect squared number have an unpair number of divisors

Question

why only perfect squared number have an unpair number of divisors

In: Mathematics

Answer 1

Because if you divide a number by its divisor, you get another divisor. Divisors are naturally paired up like this. The only way you can end up with odd number of divisors is if a divisor pairs up with itself, which means the original number is square of this divisor.