How many factors of 14,400 are divisible by 18 but not by 36?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 3.
14400 = 26 × 32 × 52
18 = 2 × 32
36 = 22 × 32
Factors of 14400 divisible by 18 = 2n × 32 × 5m, where n ≥ 1, m ≥ 0
Factors of 14400 divisible by 36 = 2n × 32 × 5m, where n ≥ 2, m ≥ 0
For n=1, m can be 0, 1, or 2
Total factors = 3