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8 of the numbers less than 660 are divisible by 5 and 11 but not 3.

All numbers divisible by 5 and 11 are multiples of their lcm; lcm(5, 11) = 55

All numbers divisibile by 5, 11 and 3 are multiples of their lcm; lcm(5, 11, 3) = 165

659 ÷ 55 = 11 54/55 → 11 numbers less than 660 are divisible by 5 and 11

659 ÷ 165 = 3 164/165 → 3 numbers less than 660 are divisible by 5, 11 and 3

→ of the 11 numbers less than 660 divisible by 5 and 11, 3 are also divisible by 3

→ 11 - 3 = 8 numbers less than 660 are divisible by 5 and 11 but not 3,.

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Q: How many natural numbers below 660 are divisible by 5 and 11 but not by 3?

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There are 43 natural numbers between 200 and 500 that are divisible by seven.

There are 39 natural numbers between 1,000 and 1,500, inclusive, that are divisible by 13.

There are 80 such numbers.

between 1 and 600 inclusive there are:300 numbers divisible by 2200 numbers divisible by 3100 numbers divisible by both 2 and 3400 numbers divisible by 2 or 3.

The first 3 digit natural number is 100: 100 ÷ 4 = 25 → first 3 digit natural number divisible by 4 is 4 × 25 The last 3 digit natural number is 999: 999 ÷ 4 = 249 r 3 → last 3 digit natural number divisible by 4 is 4 × 249 → number of 3 digit natural numbers divisible by 4 is 249 - 25 + 1 = 225.

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