Number Theory Prime Numbers and Composite Numbers Prime

Number Theory

Prime Numbers and Composite Numbers Prime Number: A whole number greater than 1, whose only factors are 1 and itself. Composite Number: A whole number greater than 1 that has more than 2 factors. 45 7 248 67 36 101 23 9 57

Prime Numbers and Composite Numbers Prime Number: A whole number greater than 1, whose only factors are 1 and itself. Composite Number: A whole number greater than 1 that has more than 2 factors. 45 7 248 67 36 101 23 9 Prime: 7, 23, 67, 101 Composite: 9, 36, 45, 57, 248 57

Greatest Common Factors in the Real World Gina is using acorns and leaves to make table centerpieces for a banquet. She wants each centerpiece to have the same number of acorns and the same number of leaves. She wants to use all the leaves and all the acorns. Gina has the number of acorns and leaves shown below. What is the greatest number of centerpieces she can make? How many acorns and leaves can she use for each centerpiece? 42 60

Greatest Common Factors in the Real World Gina is using acorns and leaves to make table centerpieces for a banquet. She wants each centerpiece to have the same number of acorns and the same number of leaves. She wants to use all the leaves and all the acorns. Gina has the number of acorns and leaves shown below. What is the greatest number of centerpieces she can make? 6 How many acorns and leaves can she use for each centerpiece? 7 acorns (7 × 6 = 42), 10 leaves (10 × 6 = 60) 42 60

Greatest Common Factor The greatest common factor (GCF) is the greatest number that is a common factor of two or more numbers. One Way to Find the GCF: List the factors of each number. Circle all the factors that the numbers have in common. The greatest factor is the GCF. 24 and 36 24: 1 36: 1 2 2 3 3 4 4 6 6 8 9 12 24 12 18 36 The GCF is 12. Find the GCF: 12 and 18 20 and 24 42 and 56

Greatest Common Factor The greatest common factor (GCF) is the greatest number that is a common factor of two or more numbers. One Way to Find the GCF: List the factors of each number. Circle all the factors that the numbers have in common. The greatest factor is the GCF. 24 and 36 24: 1 36: 1 2 2 3 3 4 4 6 6 8 9 12 24 12 18 36 The GCF is 12. Find the GCF: 12 and 18 6 20 and 24 4 42 and 56 14

Least Common Multiple The least common multiple (LCM) is the least number that is a common multiple of two or more numbers. One Way to Find the LCM: List some multiples of each number. Highlight the common multiples in each list. The least multiple (the first common multiple) in both lists is the LCM. 8 and 12 8: 8 16 24 32 40 48 56 12: 12 24 36 48 60 The LCM is 24. Find the LCM: 9 and 15 18 and 27 10 and 12

Least Common Multiple The least common multiple (LCM) is the least number that is a common multiple of two or more numbers. One Way to Find the LCM: List some multiples of each number. Highlight the common multiples in each list. The least multiple (the first common multiple) in both lists is the LCM. 8 and 12 8: 8 16 24 32 40 48 56 12: 12 24 36 48 60 The LCM is 24. Find the LCM: 9 and 15 45 18 and 27 54 10 and 12 60

Prime Factorization is the expression of a composite number as the product of its prime factors. Make a Factor Tree Divide by Prime Factors Start with any two factors. Start with the number. Keep factoring the factors until all the factors are prime. Divide by prime factors until all factors are prime. Write in exponential form. 6 54 × 9 × 3 × 100 ÷ 2 = 50 50 ÷ 2 = 25 25 ÷ 5 = 5 2 3 54 = 2 × 3 × 3 = 2 × 33 100 = 2 × 5 × 5 = 22 × 52 Find the prime factorization of each number. 36 45 120

Prime Factorization is the expression of a composite number as the product of its prime factors. Make a Factor Tree Divide by Prime Factors Start with any two factors. Start with the number. Keep factoring the factors until all the factors are prime. Divide by prime factors until all factors are prime. Write in exponential form. 6 54 × 9 × 3 × 100 ÷ 2 = 50 50 ÷ 2 = 25 25 ÷ 5 = 5 2 3 54 = 2 × 3 × 3 = 2 × 33 100 = 2 × 5 × 5 = 22 × 52 Find the prime factorization of each number. 36 22 × 3 2 45 32 × 5 120 23 × 5