Problem Solving - 8

How many factors of 2940 are NOT factors of 112?

(A) 22

(B) 30

(C) 32

(D) 34

(E) None of these

Answer - B

Prime factors of 2940 = (2 ^ 2) * 3 * 5 * (7 ^ 7)

Hence total number of factors of 2940

= (2 + 1) * ( 1 + 1) * (1 + 1) * ( 2 + 1) = 36
(by the method of counting number of factors)

Prime factors of 112 = (2 ^ 4) * 7

Therefore common factors for the above two numbers are

2^2 * 7

Total number of factors for (2 ^ 2) * 7 = (2 + 1) * ( 1 + 1) = 6

Hence total factors of 2940 which are not factors of 112 are

36 - 6 = 30, Hence B is the answer.