Problem Solving

Experts: pls an intuitivw way for solving the following:

When integer m is divided by 13 the quotient is q and the remainder is 2. When m is divided by 17 the remainder is also 2. What is the remainder when q is divided by 17?

should be zero

Yes it is zero actually. Could you elaborate a little on how you got to that answer please?

I am usually not so good with remainders but I will attempt to explain this. Please correct me if I am wrong.

When integer m is divided by 13 the quotient is q and the remainder is 2.

m = 13q + 2

When m is divided by 17 the remainder is also 2.

we can take k as a variable quotient here.

m = 17k + 2

set them equal to each other since they both equal m

13q + 2 = 17k + 2

notice that 2's cancel out, and we are left with q = (13k)/17

q and k are quotients which means they are integers. 13 is not divisible by 17 which means k is divisible by 17. since the numbers are divisible with each other, the remainder would be zero.

-hope that helps.

fantastic, thanks for sharing!