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Q: How many numbers between 150 and 500 are divisible by 2 3 and 7?

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There are 29 numbers between 1 and 150 that are divisible by five.

10 numbers

150/8 = 18.75 so 18 numbers.

20 of them.

150 ÷ 9 = 16 r 6 → the first natural number between 150 and 300 divisible by 9 is 9 × 17 (=154)300 ÷ 9 = 33 r 3 → the last natural number between 150 and 300 divisible by 9 is 9 × 33 (=297)→ there are 33 - 17 + 1 = 17 natural numbers between 150 and 300 divisible by 9.

Related questions

There are 29 numbers between 1 and 150 that are divisible by five.

10 numbers

150/8 = 18.75 so 18 numbers.

20 of them.

There are 600 5-digit numbers divisible by 150.

126

150 ÷ 9 = 16 r 6 → the first natural number between 150 and 300 divisible by 9 is 9 × 17 (=154)300 ÷ 9 = 33 r 3 → the last natural number between 150 and 300 divisible by 9 is 9 × 33 (=297)→ there are 33 - 17 + 1 = 17 natural numbers between 150 and 300 divisible by 9.

149 of them.

There are 899 numbers between 100 and 1000. Every 6th number is divisible by 6. 899 divided by 6 is 149 and 5/6. The answer must be 149 or 150. The first number in that set is 102 (17 x 6). The last is 996 (166 x 6). 166 - 17 + 1 is 150. There are 150 numbers between 100 and 1000 that are divisible by 6.

There are (500-100)/2 = 200 numbers divisible by 2 between 100 and 500 counting 100 but not 500. Of these (500-100)/8 = 50 are divisible by 8. So there are 150 numbers between 100 and 500 divisible by two but not by 8. By relative primeness exactly 50 out of these 150 are divisible by 3 and therefore these 50 are exactly the ones divisible by 6 but not by 8.

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There are ten such numbers: 110, 120, 130, 140, 150, 160, 170, 180, 190 and 200.

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