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Q: What is the smallest number that gives no remainder when divided by 7 14 or 21?

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12 is the smallest whole number that gives a remainder of 4 when it is divided by 8.

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221 is the smallest number which when divided by 24 36 and 54 gives a remainder of 5 each time

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124

8

169 is the smallest such number.

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3, when divided by 2.

The smallest number is 9361. 9361 = 40*234 + 1 9361 = 1872*5 + 1 9361 = 11*851

23, 58, 93, 128, 163, 198, ...

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23 is an odd number between 10 and 30 that gives a remainder of 2 when divided by 7.

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40

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3 divided by 2 goes once, remainder one.

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69.

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77/6 = 12 remainder 5

12*1 + 3 = 15 12*2 + 3 = 27 12*4 + 3 = 51 when 51 divided by 15 gives the remainder as 6.

200

No. Add the digits of the dividend and if that is divisible by 3 then the original number is divisible by 3; if not, its remainder when divided by 3 gives the remainder when the original number is divided by 3: 1 + 2 + 1 = 4 which gives a remainder of 1 when divided by 3, so 121 divided by 3 gives a remainder of 1. (121 = 40 x 3 + 1)

Any prime number greater than 11.