Question

The sum of all the prime factors of $m$ is 9. Find the number $m$.

• A. 15
• B. 18
• C. 28
• D. 12

Answer 1

The correct option is C 28

Factors of 15 are 1, 3, 5 and 15.
Among these the prime factors are 3 and 5.
$\therefore$ Sum of prime factors = 3+5 = 8

Similarly,
Factors of 18 = 1, 2, 3, 6, 9 and 18.
Among these the prime factors are 2 and 3.
$\therefore$ Sum of prime factors = 2+3 = 5.

Factors of 28 = 1, 2, 4, 7, 14 and 28.
Among these the prime factors are 2 and 7.
$\therefore$ Sum of prime factors = 2+7= 9.

Factors of 12 = 1, 2, 3, 4, 6 and 12
Among these the prime factors are 2 and 3.
$\therefore$ Sum of prime factors = 2+3 = 5.

We can see that the prime factors of 28 sums up to 9.
$\therefore$ The value of $m$ is 28.