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Question

How many factors of 720 are divisible by 4 but not by 16?


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Solution

Estimate the number of factors:

Factors of 720 are

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360 and720.

Out of these,

4,8,12,16,20,24,36,40,48,60,72,80,120,144,180,240,360 and 720 are divisible by4.

The number of factors divisible by4=18.

Out of these, 4,8,12,20,24,36,40,60,72,120,180,360 are not divisible16.

Hence, the number of factors divisible by 4 but not divisible by 16 is12.


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