Factoring with Prime Numbers division statements

So in my book, it has the following statements which are meant to help you do prime factoring more quickly without a calculator. (I assume.)

1. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

So this leads me to assume that it works with 2 digit through 10 digits through as many digits as your Algebra math problems can have.

Q1) Are there any limitations to statement 1?

There are others as well.

2. If a number is even and the sum of its digits is divisible by 3, the number is divisible by 6.

3. If the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

Have a great day or night as the case may be!

Re: Factoring with Prime Numbers division statements

Hey MrDiedel.

It's hard to say given that we don't know the book you are using or the context that the statement is made in (the book for example may include other information to help see how the statements are true).

Re: Factoring with Prime Numbers division statements

The book is called, "Algebra Demystified" 2nd edition, printed by McGraw Hill. Author Rhonda Huettenmueller. If you have access to this book, the statements listed above are in the appendix on page 469. The heading reads, __Factoring with Prime Numbers__. The following text is shown;

"Factoring is a skill that is developed with practice. The only surefire way to factor numbers into their prime factors is by trail and error. There are some number facts that will make our job easier. Some of these facts should be familiar."

Following this text are the statements as listed above with a few others.