Problem Solving

" If a number has a remainder of 'r', all its factors will have the same remainder 'r' provided the value of 'r' is less than the value of the factor.
Eg. If remainder of 21 is 5, then remainder of 7 (which is a factor of 21) will also be 5. "

I am trying to understand the above statement:
From the above, if 21 is divided by 8, the remainder will be 5.Since 7 is a factor of 21, the remainder when 7 is divided by 8 is supposedly also 5. But obviously, this is not the case.

Can someone explain to me clearly what the statement is actually trying to prove?

Thanks!

MakeitHappen wrote:" If a number has a remainder of 'r', all its factors will have the same remainder 'r' provided the value of 'r' is less than the value of the factor.
Eg. If remainder of 21 is 5, then remainder of 7 (which is a factor of 21) will also be 5. "

I am trying to understand the above statement:
From the above, if 21 is divided by 8, the remainder will be 5.Since 7 is a factor of 21, the remainder when 7 is divided by 8 is supposedly also 5. But obviously, this is not the case.

Can someone explain to me clearly what the statement is actually trying to prove?

Thanks!

First of all, a number does not have a remainder. When one positive integer (x) is divided by another (y), we get a quotient (k) and a remainder (r) such that 0 <= r < y

x= ky + r

or x/y = k + r/y

For example, when 33 is divided by 16, the quotient is 2 and the remainder is 1.

Note that when 33 is divided by any factor of 16 greater than 1 (i.e. 2,4,8), the remainder will also be 1