When a positive integer K is divided by 6, the remainder is 1, what is the remainder when 5K is divided by 3?

When K divide by 6 , the rmainder =
1

==> we can write the
equation:

k/6 = n + 1     where n is an
integer.

Now multiply by
6:

==> k = 6n + 6

Now
multiply by 5:

==> 5k = 30n +
30

Now divide by 3:

==>
5k/3 = 30/3n + 30/3

==> 5k/3 = 10n +
10

But 10 >3 , then the remainder should be less
<3

The remainder is either 1 or
2.

Let us rewrite 10 as multiply of
3.

==> 5k/3 = 10n + 3*3 +
1

==> 5K/3 = 10N+9  +
1

Since 10n+10 is an integer , then the
remainder is 1: