How many integers from 1 to 1000 are divisible by 30 but not by 16?

How many integers from 1 to 1000 are divisible by 30 but not by 16? Correct Answer 29

There are 1000 integers from 1 to 1000. Number of integers from 1 to 1000 divisible by 30 = 1000/30 = 33 Least common factor of 30 and 16 = 240 Number of integers from 1 to 1000 divisible by both 30 and 16 = 1000/240 = 4 Therefore, number of integers from 1 to 1000 divisible by 30 but not by 16 = 33 - 4 = 29.
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