1. ALGEBRA READINESS LESSON 4-1 Warm Up Lesson 4-1 Warm Up

2. ALGEBRA READINESS LESSON 4-1 Warm Up Lesson 4-1 Warm Up

3. ALGEBRA READINESS “Prime Factorization” (4-1) What is a “factor”? How do you find the factors of a number? factors: the numbers you multiply together to get a product. Example: the product 24 has several factors. 24 = 1 x 24 24 = 2 x 12 24 = 3 x 8 24 = 4 x 6 The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24 To find the factors of a number: Start with 1 times the number. Try 2, 3, 4, etc. If you get doubles (such as 4 x 4), then you’re done. Repeats or doubles let you know you’re done. Example: What are the factors of 16? 3 isn’t a factor Z (doesn’t go into 16), so cross it out Doubles or repeats mean your done! The factors of 16 are 1, 2, 4, 8, and 16. 1 x 16 2 x 8 3 x ? 4 x 4

4. ALGEBRA READINESS There can be 5 row of 7 seeds in each row or 7 rows of 5 seeds in each row. 1 35 Write each pair of factors. Start with 1. Skip 2, 3, and 4, because 35 is not 5 7 divisible by 2, 3, or 4. 5 is a factor. Skip 6, because 35 is not divisible by 6. 7 5 Stop when you repeat factors. You have 35 vegetable seeds to plant in your garden. The seeds must be planted in rows of equal length. How many seeds can be in each row? Look for pairs of factors of 35 to find the possible numbers of seeds in each row. Prime Factorization LESSON 4-1 Additional Examples

5. ALGEBRA READINESS “Prime Factorization” (4-1) What are “prime numbers”? What are “composite numbers:? What is “prime factorization”? prime number: numbers that only have two factors: one, and the number itself Examples: 3, 5, 7, 11, 31 composite numbers: numbers that have more than two factors Examples: 6, 15, 18, 30, 100 prime factorization: when a composite number is expressed as the product of prime numbers only Example: 18 can be expressed as 3 x 3 x 2 Example: 40 can be expressed as 2 x 2 x 2 x 5

6. ALGEBRA READINESS 61 has only two factors, 1 and 61. So 61 is prime. a. 61 b. 65 Since 65 is divisible by 5, it has more than two factors. So 65 is composite. Is each number prime or composite? Explain. Prime Factorization LESSON 4-1 Additional Examples

7. ALGEBRA READINESS 2 x 50 “Prime Factorization” (4-1) How do you find the prime factorization of a number? To find the prime factorization of a number, make a factor tree as follows:. 1.Write the product of a prime and composite number under the original number and draw lines connecting the factors with the original number 2.Circle the prime number, and repeat step 1 with the composite factor. 3.Continue this process until the only numbers you have left are prime numbers. 4.Multiply all of the circled numbers together. Example: What is the prime factorization of 100? 100 2 x 25 5 x 5 2 is a prime numbers, so we are done with it. 5 is a prime numbers, so we are done with it. So, the prime factorization of 100 is 2 x 2 x 5 x 5.

8. ALGEBRA READINESS “Prime Factorization” (4-1) How can we express prime factorization with exponents? “ Since exponents show repeated multiplication (i.e. 3 4 means “3 x 3 x 3 x 3”), write any repeated prime numbers once and use an exponent to tell how many times that multiplication is repeated. Example: In the previous example, we found the prime factorization of 100 as being 2 x 2 x 5 x 5. 2 x 2 can be expressed in exponent form as 2 2 5 x 5 can be expressed in exponent form as 5 2 So, 2 x 2 x 5 x 5 is more simply put as 2 2 x 5 2

9. ALGEBRA READINESS prime 330 prime 310 prime 2525 Find the prime factorization of 90. The prime factorization of 90 is 2 3 3 5 or 2 3 2 5. 90 Stop when all factors are prime. Use a factor tree. Because the sum of the digits of 90 is 9, 90 is divisible by 3. Begin the factor tree with 3 30. Prime Factorization LESSON 4-1 Additional Examples

10. ALGEBRA READINESS Write the prime factorization for each number. 1.362.150 3.994.225 2 2 3 2 2 3 5 2 3 2 113 2 5 2 Prime Factorization LESSON 4-1 Lesson Quiz