2. Factoring

3. Factors Factors - Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 2 · 3 = 6 6 ÷ 3 = 2 6 ÷ 2 = 3 FactorsProduct 6 is divisible by 3 and 2

4. Factoring Numbers Factoring a number means finding its factors. Basically you have to figure out what you could divide a number by without anything leftover. (no remainder). There are 2 ways to do this. (well, there are actually more… but for our purposes we are only going to look at 2)

5. Method 1: Listing List the factors in pairs. 18: 1 · 18 2 · 9 3 · 6 1 is a factor. 2 is a factor. 3 is a factor. 4 is not a factor. 5 is not a factor. 6 has already been listed. So STOP here. You can draw a diagram to illustrate the factor pairs. 18: 1 2 3 6 9 18

6. Method 2: Prime Factorization The prime factorization of a number is written as the product of its prime numbers. To find those prime numbers you create a factor tree. Like monkeys swinging on the lowest branches of the trees, prime numbers swing off the lowest branches of factor trees. * See I told you to stick with me on the monkey thing

7. Let’s say you want to factor 30. Draw two little branches coming down from the number. Ask yourself, “ What are two numbers that when multiplied together give you 30?” How about 15 and 2? Then look at both of these numbers and ask the same question. For 15 we can split it into 3 and 5. But for 2 it is already prime. Yes, like a monkey. We then circle the “monkeys” to keep track of them. And what about 3 and 5? They are both monkeys as well, so they also get circled.

8. 30 15 2 5 3 *No matter how you start a factor tree, you’ll always end up with the same prime #’s. Each of the circled numbers is prime, so we’re done. The prime factorization of 30 is 2 · 3 · 5.