Question

The number 4 is the smallest positive integer that has exactly three factors 1, 2 and 4. If k is the smallest positive integer after 4 to have exactly three factors, then find the sum of three factors of k
A) 13
B) 14
C) 16
D) 18
E) 20

Answer 1

Hint: let us proceed the question with error and trial method. As now select the number having three-factor exactly and should be greater than. So, proceed by selecting and checking the number greater than 4 and must be having three-factor.

Complete step by step solution:
All the prime no. will have 2 factors only so,
5 and 7 are rejected already.
As 5 rejected so check or 6.
Now, the factors of 6 are 1, 2, 3, 6 (as it has 4 factors so it will be rejected)
As 7 also being a prime number with two factors is also rejected and so now check for 8.
The factor of 8 is 1, 2, 4, 8 (as it has 4 factors so it will also be rejected)
Now, check for 9,
The factor of 9 is 1, 3, 9 (as it has three factors and greater than 4 so it is approved)
Hence, 9 is the number after 4 having three factors.
And the sum of the factors of 9 is
\[{\text{1 + 3 + 9 = 13}}\]
Option (a) is correct answer.

Note: Take the number that is greater than 4 and search for each and every factor of the number. It will be approved being three factors only. Trial and error is a fundamental method of problem-solving. It is characterized by repeated, varied attempts which are continued until success, or until the practitioner stops trying.