Originally Posted by

**fair_lady0072002** The product of any whole numbers each of which leaves a remainder of 1 on dividing by 8, also leaves a remainder of 1 on dividing by 8. Why?

First I picked the any two numbers that leave a remainder of 1 on dividing by 8;

9 and 17

9 x 17 = 153 also leaves a remainder of 1 on dividing by 8.

Then I did; 9 = 8 + 1; also 17 = 16 + 1

and 9 x 17 = (8 + 1) x (16 + 1) = (8 x 19) + 1

I am stuck on how to explain how this is so, not sure if there is another way of presenting this.

Thank you for the help.