Unit 1; Part 2:Using Factors for

Fractions and Solving Problems

You need to be able to findthe GCF, LCM and solveproblems using them.

Advanced Homework Answers – pp. 199-200

4. 51 (3 x 17) 16. Composite

5. Prime 17. Composite

6. Composite 18. Prime

7. Prime 19. Prime

13. Composite 20. Prime

14. Composite 42. False; 2 is prime.

15. Prime 51. Composite

Unit 1, Lesson 8 – AdvancedPrime Factorization

Assignment – pp. 199-200;

#3, 21-35 odd, 39-41, 44-48.

ReviewPrime Numbers- A Prime number is a whole number with

only 2 factors, one and itself.

A Composite number is a number that has more than two factors.

Examples: 2, 3, 5, 7, 11, 13, 17, 19…

Composite Numbers-

Example: 4, 6, 8, 9, 10, 12, 14, 15…

Prime Factorization• Prime Factorization is the unique

set of prime numbers whose product equals a given composite number.

• To find the prime factorization, the number must be split up using a factor ladder.

• No factor trees allowed!

Factor Ladders

• Use primes IN ORDER.

Prime Factorization

Write the number to be factored with an upside down division sign.

Begin with 2. Divide until the number is odd.

Move on to 3, then 5, then 7, etc. When you get to 1, you are through. The numbers down the side are the

prime factorization. They are already in order.

Prime Factorization

2412 6

3 1

2))2

))

32

23 x 3

23 x 52

Prime Factorization

200100 50

25 5 1

2))2

))

5

2

)5

2 x 33 x 5

Prime Factorization

270135 45

15 5 1

2))3

))

5

3

)3

3 x 5 x 7 x 13

Prime Factorization

1365455 91

13 1

3))5

))7

13

Factor Ladders• Find the prime factorization of 24.

The prime factorization is

23 x 3

Factor Ladders• Find the prime factorization of 50.

The prime factorization is

2 x 52

Factor Ladders• Find the prime factorization

of 252.

The prime factorization is

22 x 32 x 7

Factor Ladders• Find the prime factorization

of 144.

The prime factorization is

24 x 32

Factor Ladders• Find the prime factorization

of 1155.

The prime factorization is 3 x 5 x 7 x 11

Find the prime factorization of 100.

Answer: The prime factorization of 100 is

Find the prime factorization of 72.

Answer:

Factor LaddersTo finish a factorization:

2 x x 5 = 270

Divide by the numbers you have.

270 ÷ 2 = 135 ÷ 5 = 27

Write using primes.

27 = 33

• Find the value of the .• x 5 x 11 = 440

• 440 ÷ 5 = 88 ÷ 11 = 8

• 8 = 23

Factor Ladders• If you are asked to factor an

algebraic expression, write the number in primes, then include the variables one at a time.

• Example:

24ab2c = 23 • 3 • a • b • b • c

ALGEBRA Factor

Answer:

ALGEBRA Factor

Answer:

Note Cards for Unit 1-Lesson 8

1-31. Prime Factorization A unique set of prime numbers

whose product equals a given

composite number.

Example: 24 = 23 x 3

Advanced Homework Answerspp. 199-200

3. 9 is not prime. 39. 7

21. 22 · 32 40. 32

23. 32 · 11 41. 52

25. 2 · 3 · 5 · 7 44. 120 ft2

27. 2 · 32 · 7 45. 23 · 3 · 5

29. Composite 46. 2 by 3 or 2 by 5

31. 2 · 2 · 5 · p · q 47. 20 2x3’s or 12 2x5’s

33. 7 · 7 · y · y 48. Prime if n = 1;

35. 2 ·2 ·2 ·2 ·3 ·a ·a ·b ·b Composite if n > 1

since 2 is a factor of each.