When a number "n" is divided by 5, the remainder is 0 and when three times a number "n" is divided by 5 the remainder is what?

Since it’s not homework, the answer is 0.

Still zero.

Here’s a tip: If a formal exercise like the one you posted seems too difficult, as a first step just come up with an example to get a feeling. While this is no formal proof, it can help your thinking.

So how about we choose n = 15?

15 / 5 = 3 remainder 0
45 / 5 = 9 remainder 0

Here is a way of thinking about it. Having a remainder of 0 means that n is divisible by 5. n equals 5 times something. Multiplying n by 3 gives you a number 3×5 x something. It is still divisible by 5, and will therefore still have a remainder of 0 when divided by 5.

It’s still zero.
If ‘n’ is divided by 5 so the reminder will be zero and its only possible if the ‘n’ comes on the multiplication of 5.
Now, if 3 is multiply with any digit i.e ‘n’ always gives the answer which multiply with 5.
Hence, its answer will be zero.
Example: Suppose n= 5,
n/5 i.e 5/5 reminder will be zero
Now, 3*n=3*5=15
15/5 result will be ‘0’

A problem just teaching you about multiples of 5.

n = many integers that end in 5.

@Neodarwinian End if 5 or 0.

@Dutchess_III

Uh, strictly speaking no. That is why I said 5, as 5 also ends in 5

0 ends in 0, so…,

0/5 is undefined. 5/5 = 1, no remainder.

Strictly defined as math needs to be.

Something is missing in the discussion. Simply stated, when you divide two numbers and the answer is zero, one of them has to be zero. No remainder cluttering the problem. 3n is the same as saying three times zero. The answer is still zero, whether by itself or multiplied by another number.