# Number Theory

• July 20th 2012, 06:25 AM
timkuc
Number Theory
If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

Ans. - 1 why ?

Confusion here =>

N/15 = 15k + 7

Multiplying both side by 9

3N/5 = 5 (27k)+63 ;

3N/5 = 5 K + 3 ;

so remainder should be 3

What to do??
• July 20th 2012, 06:32 AM
a tutor
Re: Number Theory
Quote:

Originally Posted by timkuc
If a number is divided by 15 , it leaves a remainder of 7. If thrice the number is divided by 5,then what is the remainder ???

Ans. - 1 why ?

Confusion here =>

N/15 = 15k + 7

Multiplying both side by 9

3N/5 = 5 (27k)+63 ;

3N/5 = 5 K + 3 ;

so remainder should be 3

What to do??

You should have N=15k+7

and then 3N=45k+21

and so 3N=5 (9k+4) + 1.
• July 20th 2012, 06:34 AM
timkuc
Re: Number Theory
shame on me.. hattttt

btw thanks
• July 20th 2012, 08:55 AM
richard1234
Re: Number Theory
$N \equiv 7 (\mod 15)$, so it follows that $N \equiv 7 \equiv 2 (\mod 5)$.

Therefore, $3N \equiv 6 \equiv 1 (\mod 5)$ so a remainder of 1 results.