1. Factoring For use with section 1.2 Discovering Mathematics Book 1A The Brandywine School District Mathematics Department presents

3. What do we mean when we ask you to find the factors of a number? Example: Find the factors of the number

4. Let’s look at how many ways we can arrange these six items into a rectangular array. 1 row of 6 or 6 rows of 1 1 and 6 are both factors of the number 6 Can we make any other rectangular arrays with six objects?

5. 2 rows of 3 Let’s look at how many ways we can arrange these six items into a rectangular array. or 3 rows of 2 2 and 3 are both factors of the number 6 Can we make any other rectangular arrays with six objects?

6. The factors of the number are 1, 2, 3, and 6

7. You try it! Find the factors of the number

8. The factors of the number 8 are 1, 2, 4, a nd 8

9. Do all whole numbers have exactly four factors? Can you find a number with fewer than four factors ? Can you find a number with more than four factors ?

10. Can you find a number with fewer than four factors ? 11 7 5 3 2 1 13 17 19 and many many more!

11. Can you find a number with more than four factors ? 1 2 1 and 12 are factors of 12 2 and 6 are factors of 12 3 and 4 are factors of 12 12 has six factors: 1, 2, 3, 4, 6, and 12.

12. Numbers with exactly two factors are called Prime Numbers

13. 11 7 5 3 2 1 13 17 19 and many many more! Which of these numbers are PRIME NUMBERS?

14. 1 Why isn’t PRIME? The number 1 has only one factor! Prime numbers have exactly two factors.

15. Whole numbers greater than one that aren’t prime numbers are called Composite Numbers.

16. Writing whole numbers as the products of prime numbers! Recall: The factors of the number 6 are 1, 2, 3, and 6 Only two of those factors are prime numbers. The prime factorization of six is 2 x 3

17. You try it! Write the Prime Factorization of the following Composite Numbers: 910 21 22

18. You try it! Write the Prime Factorization of the following Composite Numbers: 812 16 24 Not Prime