+0

# Divisors

0
283
1

What is the least positive odd integer with exactly nine natural number divisors?

Dec 18, 2018

#1
+22528
+8

What is the least positive odd integer with exactly nine natural number divisors?

$$\begin{array}{|rcll|} \hline number &=& p^{\color{red}2}q^{\color{red}2} \\ divisors &=& ({\color{red}2}+1)({\color{red}2}+1) = 9 \\ \hline \end{array}$$

The least odd prime numbers are: 3 and 5.

$$\begin{array}{|rcll|} \hline number &=& 3^{\color{red}2}5^{\color{red}2} \\ number &=& 9\cdot 25 \\ \mathbf{number} & \mathbf{=} & \mathbf{225} \\ \hline \end{array}$$

Divisors 225:
1 | 3 | 5 | 9 | 15 | 25 | 45 | 75 | 225 (9 divisors)

Dec 18, 2018