Question
How many factors of 72000 are divisible by 36 but not 72?
Solution
72000 = 26Â x 32 x 53Â = 36 x (24Â x 53) So, number of factors divisible by 36 = (4 + 1) x (3 + 1) = 20 Also, 72000 = 72 x (23Â x 53) So, number of factors divisible by 72 = (3 + 1) x (3 + 1) = 16 Required number of factors = 20 - 16 = 4
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