How many positive integers between 100 and 999 inclusive are divisible by three or four?

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11-03-2018
Mathematics

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How many positive integers between 100 and 999 inclusive are divisible by three or four?

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Аноним Аноним · Answer 1 · 2018-03-11T14:43:50+01:00

999 - 100 + 1 = 900
There are 900 numbers between 100 and 999 (inclusive)

We group the numbers into groups of 3s. So we find one number divisible by 3 in every group.
Number of numbers that can be divided by 3 = 900 ÷ 3 = 300
Number of numbers that can be divided by 3 = 300

We group the numbers into groups of 4s. So we find one number divisible by 4 in every group.
Number of numbers that can divided by 4 = 900 ÷ 4 = 225
Number of numbers that can divided by 4 = 225
Among the group of 4s, there is 1/3 that are already inclusive in divisible by 3.
225 ÷ 3 = 75
Number of numbers that can divided by 4 = 225 - 75 = 150

Total numbers of positive integers divisible by three and fours = 300 + 150 = 450