Question

What are the possible values of remainder r, when a positive integer p is divided by 3 ?

Answer 1

Answer:

Understand what division means:

If you divide a number by 3, it means you wanna make groups of 3 out of that number

Example: 12 divided by 3 means you can make 4 groups of 3 from the number 12.

So, that being said, if you divide something by 3, the remainder can be either 1 or 2.

Example:

14/3 will leave a remainder of 2, because uptill 12 you can make 4 groups of 3 but 2 will be left incomplete.

As soons as the number becomes 15, the remainder 2 will get 1 extra, and a new group of 3 will be made leaving no remainder.

So, you cannot get a reminder greater than the divisor 3. Anything greater than 3 would easily make a group of 3, and will leave either 1 or 2.

One thing you wanna know is, there are negative remainders too.

If you get an remainder of 2, it means you need 1 more to make a group. So the alternate remainder becomes -1. If reflects the shortage that is causing a remainder 2 and is written with a (-) sign.

So, if a remainder is 1, then the alternate remainder will be -2. Because, 2 is what is lacking from it to become complete group of 3.

Hope you understand.