Question

When a positive integer k is divided by 6, the remainder is 1. What is the remainder when 5k is divided by 3?

Answer 1

Answer:

$3$

Step by step explanation:

According to the task, $k = 6n+1$, $n$ is an integer. $5k = 30n + 5=3*10n+3*1+2=3(10n+1)+2$. That`s why $5k$ has a remainder $2$ when it is divided by $3$.

Answer 2

To find the remainder when 5k is divided by 3, we can use the information that when k is divided by 6, the remainder is 1.

Let's express k in terms of 6:

k = 6n + 1, where n is a non-negative integer (because k leaves a remainder of 1 when divided by 6).

Now, we want to find the remainder when 5k is divided by 3:

5k = 5(6n + 1) = 30n + 5

To find the remainder when 30n + 5 is divided by 3, we can focus on the remainder of the term 5 when divided by 3. The remainder when 5 is divided by 3 is 2.

So, when 5k is divided by 3, the remainder is 2.

In summary, the remainder when 5k is divided by 3 is 2.