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

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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:

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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:

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