## Cute Number

A number is called cute if it has exactly four positive integral divisors. What percent of the first twenty-five positive integers are cute?
Source: NCTM Mathematics Teacher, January 2006

SOLUTION
$22=2^1\!\cdot\! 11^1$
$(1+1)(1+1)=4$ number of factors/divisors
$21=3^1\!\cdot\! 7^1$
$(1+1)(1+1)=4$
$15=3^1\!\cdot\! 5^1$
$(1+1)(1+1)=4$
Other integers that have $4$ factors/divisors: $14,10,8,6$.
Total number of integers that have $4$ divisors equals $7$.
Percent of the first twenty-five positive integers that are cute
$7/25=28\%$

Answer: $28\%$