\(\displaystyle N\) is an integer greater than 5.
When 205 is divided by \(\displaystyle N\), the remainder is 5.
For how many distinct positive integers \(\displaystyle N\) is this statement true?
\(\displaystyle \text{I know given: }\:\frac{205}{N} \:=\: m + \frac{5}{N},\:m\text{ is an integer.}\)
Then what to do?
soroban said:Hello, brucejin!
You're on your way . . .
\(\displaystyle N\) is an integer greater than 5.
When 205 is divided by \(\displaystyle N\), the remainder is 5.
For how many distinct positive integers \(\displaystyle N\) is this statement true?
\(\displaystyle \text{I know given: }\:\frac{205}{N} \:=\: m + \frac{5}{N},\:m\text{ is an integer.}\)
Then what to do?
Multiply your equation by \(\displaystyle N\!:\;\;205 \:=\:mn + 5 \quad\Rightarrow\quad Nm \:=\:200\)
Hence, \(\displaystyle N\) is a factor of 200, where \(\displaystyle N > 5.\)
Therefore: .\(\displaystyle N \;=\;8, 10, 20, 25, 40, 50, 100, 200\quad\hdots \quad \boxed{8}\text{ values.}\)
soroban said:\(\displaystyle N \;=\;8, 10, 20, 25, 40, 50, 100, 200\quad\hdots \quad\)
bom?bas?tic?mmm4444bot said:My bombastic opinions, of course.
You forgot stapelmmm4444bot said:...Better yet, it's time for Soroban, Glenn, Eddie, Arthur, et al, ...
mmm4444bot said:Also, Soroban consistently advertises that he's the other guy who completes students' homework, but who's the first guy?
Denis said:You forgot stapelmmm4444bot said:...Better yet, it's time for Soroban, Glenn, Eddie, Arthur, et al, ...
YES, you're missing my "joke like" intent...stapel is "cruel"Subhotosh Khan said:Denis - I might be missing your point totally - but stapel is one of the tutors who insists on having work shown.
brucejin said:… sorry for my tough question which caused you guy so much trouble.