A number theory problem by Syed Baqir

Number Theory Level 1

When a positive integer k is divided by 5 the remainder is 3, what is the remainder when 3k is divided by 5 ?


The answer is 4.

Syed Baqir by Syed Baqir , 24, Cyprus

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5 solutions

Sai Raghava Puni
Jul 7, 2015

let k=5n+3....... then 3k=15n+9........hence 3k/5=(15n+9)/5=3n+9/5 hence remainder is 4

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Syed Baqir
Jul 5, 2015

We can find the answer by trying some numbers, such as : 8, 13 , and 18 == K+5=3 so 8/ 5 = 3 13/5 = 3 (remainder) therefore, 3K = 8*3 = 24 similarly , 39 , 54 HENCE 24/5 =4 (remainder) similar case for others

3 Helpful 0 Interesting 0 Brilliant 0 Confused

yes .its that much easy and quick

Rohit Udaiwal - 5 years, 10 months ago
Brian Leibowitz
Aug 3, 2015

k = 3mod5; 3k = 9mod5 = 4mod5

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Debanjan Dey
Jul 15, 2015

Did'nt solve anything, I just took k as 8 and then divided 24(=8*3) by 5 to get 4 as remainder. Since k is variable, it can be number similar to 8.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Saleem
Jul 8, 2015

All you have to do is get an example. Hmm, remainder of 3? 18 works! Now what is the remainder of 18*3/5? 4!

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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