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\%

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About mvtrinh

Retired high school math teacher.
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