1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Write each number as a product of two whole numbers in as many ways as possible.
1. 6
2. 16
3. 17
4. 36
1  6, 2  3
1  16, 2  8, 4  4
1  17
1  36, 2  18, 3  12, 4  9, 6  6

3. California
Standards
Preparation for Number Sense (NS2.4) - Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction).

4. Objective: You will learn how to find the prime factorization of composite numbers.

5. Vocabulary
prime number
composite number
prime factorization

6. A prime number is a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3.
A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors—1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite.

7. Tell whether each number is prime or composite.
Example 1: Identifying Prime and Composite Numbers
Tell whether each number is prime or composite.
A. 11
B. 16
The positive factors of 11 are 1 and 11.
The positive factors of 16 are 1, 2, 4, 8, and 16.
11 is prime.
16 is composite.

8. Tell whether each number is prime or composite.
Check It Out! Example 2
Tell whether each number is prime or composite.
A. 14
B. 7
The positive factors of 14 are 1, 2, 7, and 14.
The positive factors of 7 are 1 and 7.
14 is composite.
7 is prime.

9. A composite number can be written as the product of its prime factors
A composite number can be written as the product of its prime factors. This is called the prime factorization of the number.
You can use a factor tree to find the prime factors of a composite number.
You can also use the “Stairs Method” to find the prime factors of a composite number.

10. You can write prime factorization by using exponents
You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.
Writing Math

11. Write the prime factorization of the number 24.
Example 3: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number 24. 24
8  3
4  2
2  2
The prime factorization of 24 is 2  2  2  3 or 23  3.

12. Write the prime factorization of the number 90.
Check It Out! Example 4
Write the prime factorization of the number 90. 90
45  2
9  5
3  3
The prime factorization of 90 is 3  3  5  2, or 2  32  5.

13. Write the prime factorization of the number 150.
Example 5: Using a Factor Tree to Find Prime Factorization
Write the prime factorization of the number 150.
150
30  5
10  3
2  5
The prime factorization of 150 is 2  3  5  5, or 2  3  52.

14. Check It Out! Example 6
Write the prime factorization of the number 225.
225
45  5
9  5
3  3
The prime factorization of 225 is 3  3  5  5, or 32  52.

15. You can also use the “Stairs Method” to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

16. Write the prime factorization of the number 476.
Example 7: Using the “Stairs Method” to Find Prime Factorization
Write the prime factorization of the number 476. 2
476 2
238 7
119 17 17 1
The prime factorization of 476 is 2  2  7  17, or 22  7  17.

17. There is only one prime factorization for any given composite number
There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 2
476 7
476 2
238 2 68 7
119 2 34 17 17 17 17 1 1
The prime factorizations are 2  2  7  17 and
7  2  2  17, which are the same as 17  2  2  7.

18. Example 8: Using the “Stairs Method” to Find Prime Factorization
Write the prime factorization of the number 275. 5
275 5 55 11 11 1
The prime factorization of 275 is 5  5  11, or 52  11.

19. Check It Out! Example 9
Write the prime factorization of the number 324. 2
324 2
162 3 81 3 27 3 9 3 3 1
The prime factorization of 324 is 2  2  3  3  3  3, or 22  34.

20. The prime factorization of 325 is 5  5  13, or 52  13.
Check It Out! Example 10
Write the prime factorization of the number 325. 5
325 5 65 13 13 1
The prime factorization of 325 is 5  5  13, or 52  13.

21. Prime Wars
Home Learning
On-Line Tutoring
Factor Trees
Factor Game

22. Lesson Quiz
Tell whether each number is prime or composite.
prime
composite
composite
Write the prime factorization of each number. 33
22  32
22  7
22  3  11
22  13
22  33