How many numbers between one and 100 are divisible by three or seven?

There are 43 numbers between one and 100 that are divisible by three or seven. These numbers include 29 numbers that are only divisible by three, 10 numbers that are only divisible by seven, and four numbers that are divisible by both three and seven.

To work out how many numbers between one and 100 are divisible by three, divide 100 by three and round the result down to the nearest whole number. This is 33. Work out how many numbers between one and 100 are divisible by seven in the same way. This result is 14. Subtract the number of numbers that are divisible by both three and seven, of which there are four: 21, 42, 63 and 84.