# 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:

==> 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:**

When K is divided by 6 the remainder is 1.

We can therefore write K as 6a+1, where a is a whole number.

Now 5K can be written as 5*(6a+1)=30a+5

When 5K is divided by 3 it is the same as dividing (30a+5) by 3 or (30a+5/3 which is equal to 10a+5/3. Now 10a is a whole number, 5/3 can be written as 1+ 2/3.

Therefore 5K/3= 10a +1+ 2/3.

Therefore the remainder is 2.

**The required answer is 2.**

When K is divided by 6, remainder is 1.

So K = 6n+1.

Therefore 5K = 6(n*5) +5we get a remainder 5.

5k = 3*(2*n*5) + 3+2

5 k = 3 (10n+1)+2.

Therefore 5k / 3 = (10n+1) is quotient and Remainder = 2.