# Math homework help -factors, primes andcomposites, prime factorization

Students send me scans (or cell phone pictures) of their math homework with their own answers written down. I review and rectify mistakes, if any so that they have all correct answers by the time they turn them in to their school teachers. I also make efforts to explain the concepts/steps briefly.

Note that this is a paid service but costs significantly less than live tutoring sessions. Here are a few examples from pre algebra to show what I receive and what I send back. You can use these solutions as solved examples to learn on your own. Don't miss out on the tips and tricks, if any.

#### Word problems related to factors What I received What I sent back click on pictures to enlarge

#### Prime factors and exponents What I received What I sent back click on pictures to enlarge

#### Prime factorization with exponents, primes and composites What I received What I sent back click on pictures to enlarge

#### Primes and composites What I received What I sent back click on pictures to enlarge

Tip: A quick way to figure out if 3 can divide a number without leaving a remainder is to add up all the digits in the number and check if 3 can divide the sum obtained without leaving a remainder.

For example, to check if 3 can go into 93, add 9 with 3. Since 9 + 3 = 12 and 3 can divide 12, 3 can also divide 93 without leaving a remainder.

Similarly, 3 can't divide 145 because 1+4+5 = 10 and 3 can't divide 10.

In almost the same way, if you want to quickly find out if 9 can divide a number without leaving a remainder, add up the digits in the number. If 9 can divide the sum thus obtained, then 9 can also divide the given number.

For example, to check if 9 can go into 456, do 4 + 5 + 6 = 15. Since 9 can't divide 15, it can't divide 456 either.

Note: The tricks mentioned above work only for 3 and 9. Never try to apply these rules to find out if any other number can divide a given number. For example, if you want to find out if 4 can divide 124, you don't add 1, 2 and 4. The divisibility rule for 4 is different. We can talk about that on another day.