Question

The number 4 is the smallest positive integer that has exactly three factors: 1, 2, and 4. If k is the next-highest integer that also has exactly three factors, what is the sum of the three factors of k

Answer 1

To solve this problem, we must do a method of trial and error to find for the next highest integer with exactly three factors. We know that the value of k must be greater than 4, therefore by using trial and error to find for the correct answer:

 

Factors of 5:1, 5

Factors of 6:1, 2, 3, 6

Factors of 7:1, 7

Factors of 8:1, 2, 4, 8

Factors of 9:1, 3, 9

 

Therefore we stop at 9 since this is already our answer. It has exactly three factors.

The sum of the factors is:

sum of factors = 1 + 3 + 9

sum of factors = 13