Question

what is the smallest number that gives a remainder of 3 when divided by 5 and a remainder of 2 when divided by 8​

Answer 1

What is the smallest number that leaves a remainder of 2 when divided by 3, 4, 5, and 6?

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2 is the smallest one as 0*3 = 0*4 = 0*5 =0*6 = 0.

The next one is 62.

Let see:

3x + 2 = 4y+2 = 5z+2 = 6t+2.

4y +2 -> so the number should be even. (1)

5z + 2 -> the number should end with 2 or 5. (2)

From (1) and (2) -> the number should end with 2.

so the number should be something like: 10*A +2.

10*A +2 divide to 3 remain 2 so:

A+2 divide to 3 should remain 2 => we can choose A as 0, 3, 6, 9…

so we have the result:

2;

32: can divided to 4 -> not an answer.

62;

92 can divided to 4 -> not an answer.