7.3 Prime Factorization (p.168-169)

I. Use a factor tree to find the prime factors
A. Steps for prime factorization

1. Choose any two factors (other than the 1) for the number in question. Draw two lines, like branches, down from the original number and write the factors at the ends of the lines.
2. Check the numbers at the ends of the branches to see if they are prime or comoposite numbers. If they are prime, circle them to include as prime factors.
3. Draw two more branches out of all composite factors until you only have prime factors at the ends of the branches.

B. You will always end up with the same prime factors (not necessarily in the same order), regardless of the composite factors you start with.

-Below are two different examples of how you could find the prime factors for the number 700.

7.2 Prime and Composite Numbers

I Prime Number
- a whole number that only has two factors: 1 and itself

II. Composite Number
- a whole number that has at least three factors
- All even numbers, except for 2, are composite numbers

***0 and 1 are neither prime or composite

Scroll down on this site from AAAmath.com to take a quiz on prime and composite numbers

7.1 Divisibility

Divisibility Rules:

1. All numbers are divisible by 1
2. If the last digit is even (0,2,4,6,or8) it is divisble by 2
3. If the sum of the digits is divisible by 3, then so is the original number
4. If the last two digits form a number divisible by 4
5. If the last digit is 0 or 5
6. If the number is divisible by 2 and 3
7. Double the last digit and subtract it from the rest of the digits. (Repeat the process
   for larger numbers.) If you get a # that is divisible by 7, then so is the number.
8. If the last three digits form a number divisible by 8
9. If the sum of the digits is divisible by 9
10. If the last digit is 0

Test what you know by applying the divisibility rules for 10 practice numbers at vectorkids.com

Chapter 7 Video Tutorial

Here is a rather lengthy video that covers most of the materials in chapter 7.