How can u tell if a quotient has a remainder without dividing

Some numbers just don't fit into other numbers perfectly. 3 does not go into 7 perfectly. It goes into 6 perfectly, but not 7.

When you get division problems such as 7 divided by 3, expect to deal with remainders. Just by looking at those two numbers, you can see that there is something wrong. 3 goes into 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, etc, etc. It just isn't in harmony with 7...

It's important to learn your times tables so that you can automatically distinguish numbers that are in harmony and those that aren't.

I never thought about that.  But here's one way you could do it, that might even
be related to some of the math you're doing in school just now:

-- Take the number that has to be divided.

-- Find all of its factors.

-- If you divide it by one of its factors, then there will be no remainder.

-- If you divide it by any other number, then there will be a remainder.