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?
Number properties
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- ssmiles08
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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.
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.