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**Find the prime factorization of a composite number.**• prime number • composite number • prime factorization • factor tree**Factor: Factors are the numbers you multiply together to get**another number • Example:**Prime Number: A whole number greater than 1 that has exactly**two factors, 1 and itself. This means, that it can be divided by only two numbers, 1 and itself. • Prime Numbers less than 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.**Composite Number: A whole number greater than 1 that has**MORE THAN TWO factors. This means, that it can be divided by MORE THAN TWO numbers. • Composite numbers less than 100: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100**Prime Factorization: Prime Factorization is finding which**prime numbers multiply together to make the original number. • What are the prime factors of 12? 12 = 2 ● 2 ● 3 12 = 22● 3 • What are the prime factors of 72? 72 = 3 ● 3 ● 2 ● 2 ● 2 72 = 23● 32**Identify Numbers as Prime or Composite**Determine whether the number 63 is prime or composite. Answer: The number 63 has six factors: 1, 3, 7, 9, 21, and 63. So, it is composite. BrainPOP:Prime Factorization Lesson 1 Ex1**Determine whether the number 41 is prime or composite.**• A • B • C • D A. prime B. composite C. both D. neither Lesson 1 CYP1**Determine whether the number 29 is prime or composite.**• A • B • C • D A. prime B. composite C. both D. neither Lesson 1 CYP2**Find the Prime Factorization**Find the prime factorization of 100. Method 1 Use a factor tree. 100 50 × 2 25 × 2 × 2 52● 22 5 × 5 × 2 × 2 Lesson 1 Ex3**Find the prime factorization of 72.**• A • B • C • D A. 8 × 9 B. 22× 33 C. 23× 32 D. 22× 32 Lesson 1 CYP3**Factor an Algebraic Expression**ALGEBRAFactor 21m2n. 21m2n 21 × m2n 3 × 7 × m2× n 3 × 7 ×m×m× n Answer: 21m2n = 3 ● 7● m● m● n Lesson 1 Ex4**ALGEBRA Factor 15xy3.**• A • B • C • D A. 15 ● x ● y3 B. 15 ● x ● y ● y ● y C. 3 ● 5● x3 ● y D. 3 ● 5● x ● y ● y ● y Lesson 1 CYP4**Find the greatest common factor of two or more numbers.**• Venn diagram • greatest common factor (GCF) Lesson 2 MI/Vocab**Find the Greatest Common Factor**Find the Greatest Common Factor (GCF) of 28 and 42. Method 1 List the factors of the numbers. Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCF is 14. Lesson 2 Ex1**Find the Greatest Common Factor**Method 2 Use prime factorization. Write the prime factorization. Then circle the common factors. 28 = 2 ● 2 ● 7 42 = 2 ● 3 ● 7 The greatest common factor or GCF is 2 ● 7 = 14. Answer: 14 Lesson 2 Ex1**Find the GCF of 18 and 45.**• A • B • C • D A. 3 B. 9 C. 18 D. 45 18 = 3 ● 3 ● 2 45 = 3 ● 3 ● 5 The greatest common factor or GCF is 3 ● 3 = 9. Lesson 2 CYP1**Find the GCF of Three Numbers**Find the GCF of 21, 42, and 63. Method 1 List the factors of the numbers. factors of 21: 1, 3, 7, 21 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 factors of 63: 1, 3, 7, 9, 21, 63 The greatest common factor or GCF is 21. Lesson 2 Ex2**Find the GCF of Three Numbers**Method 2 Use prime factorization. 21 = 3● 7 42 = 2 ● 3 ● 7 63 = 3 ● 3 ● 7 Circle the common factors. The common prime factors are 3 and 7. Answer: The GCF is 3 ● 7 = 21. Lesson 2 Ex2**Find the GCF of 24, 48, and 60.**• A • B • C • D A. 2 B. 4 C. 6 D. 12 24 = 2 ● 2 ● 2 ● 3 48 = 2 ● 2 ● 2 ● 2 ● 3 60 = 2 ● 2 ● 3 ● 5 The GCF is 2 ● 2 ● 3 = 12. Lesson 2 CYP2**ARTSearra wants to cut a 15-centimeter by 25-centimeter**piece of tag board into squares for an art project. She does not want to waste any of the tag board and she wants the largest squares possible. What is the length of the side of the squares she should use? The largest length of side possible is the GCF of the dimensions of the tag board. 15 = 3 × 5 25 = 5× 5 The GCF of 15 and 25 is 5. Answer: Searra should use squares with sides measuring 5 centimeters. Lesson 2 Ex3**CANDY Alice is making candy baskets using chocolate hearts**and lollipops. She has 32 chocolate hearts and 48 lollipops. She wants to have an equal number of chocolate hearts and lollipops in each basket. Find the greatest number of chocolate hearts and lollipops Alice can put in each basket. • A • B • C • D A. 8 B. 16 C. 48 D. 96 48 = 2 ● 2 ● 2 ● 2 ● 3 32 = 2 ● 2 ● 2 ● 2 ● 2 Lesson 2 CYP3**Solve problems by making an organized list.**Lesson 3 MI/Vocab**Make an Organized List**PASSWORDIn order to log on to the computer at school, Miranda must use a password. The password is 2 characters. The first character is the letter A or B followed by a single numeric digit. How many passwords does Miranda have to choose from? Explore You know that the password has 2 characters and that the first character is either the letter A or B. You know that the second character is a numeric digit. You need to know how many passwords can be created. Plan Make an organized list. Lesson 3 Ex1**Make an Organized List**Solve Answer: There are 20 possible passwords. Check Draw a tree diagram to check the result. Lesson 3 Ex1**DELI At a deli, customers can choose from ham or turkey on**wheat, rye, or multi-grain bread. How many sandwich possibilities are there? • A • B • C • D A. 3 B. 4 C. 6 D. 12 Lesson 3 CYP1**Write fractions in simplest form.**• equivalent fractions • simplest form Lesson 4 MI/Vocab**What is a fraction**A fraction names a part of an object.**Numerator**Denominator**=**Remember that the denominator can not be zero**A fraction with a numerator of 0 equals 0.**0 0 = 0 = 0 4 156 Fractions**What is an equivalent fraction?**• Two fractions that stand for the same number**The fraction is in simplest form since 4 and 15 have**no common factors greater than 1. Write a Fraction in Simplest Form Method 1 Divide by common factors. 3 is a common factor of 12 and 45, so divide by 3. Lesson 4 Ex1**Write a Fraction in Simplest Form**Method 2 Divide by the GCF. First, find the GCF of the numerator and denominator. factors of 12: 1, 2, 3, 4, 6, 12 factors of 45: 1, 3, 5, 9, 15, 45 The GCF of 12 and 45 is 3. Then, divide the numerator and the denominator by the GCF. Answer: Lesson 4 Ex1**A.**B. C. D. • A • B • C • D Lesson 4 CYP1**Write a Fraction in Simplest Form**First, find the GCF of the numerator and denominator. 40 = 2 ● 2 ● 2 ● 5 64 = 2 ● 2 ● 2 ● 2 ● 2 ● 2 GCF: 2 ● 2 ● 2 = 8 Then, divide the numerator and denominator by the GCF, 8. Answer: Lesson 4 Ex2**A.**B. C. D. • A • B • C • D Lesson 4 CYP2**MUSICTwo notes form a perfect fifth if the simplified**fraction of the frequencies of the notes equals If note D = 294 Hertz and note G = 392 Hertz, do they form a perfect fifth? The slashes mean that part of the numerator and part of the denominator are both divided by the same number. For example, 7 ÷ 7 = 1 Lesson 4 Ex3**A.**B. C. D. MARBLES In a bag of 96 marbles, 18 of the marbles are black. Write the fraction of black marbles in simplest form. • A • B • C • D Lesson 4 CYP3**Find the least common multiple of two or more numbers.**• multiple • least common multiple (LCM) Lesson 8 MI/Vocab**The product of a number and any other number.**Some multiples of 6 6, 12, 18, 24, 30, 36, 42 Multiple**5, 10, 15, 20, 25, 30, 35**Some multiples of 5**9, 18, 27, 36, 45, 54, 63**Some multiples of 9**The smallest number that is a multiple of two or more**numbers. 5 = 5, 10, 15, 20, 25, 30 6 = 6, 12, 18, 24, 30, 36 Least Common Multiple (LCM)**Find the LCM**Find the LCM of 4 and 6. Method 1 List the nonzero multiples. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, . . . Multiples of 6: 6, 12, 18, 24, 30, 36, . . . LCM of 4 and 6 is 12. Lesson 8 Ex1