2 4 Prime Factorization Warm Up Problem of

2 -4 Prime Factorization Warm Up Problem of the Day Lesson Presentation Course 2

2 -4 Prime Factorization Warm Up Write each number as a product of two whole numbers in as many ways as possible. 1. 6 1 · 6, 2 · 3 2. 16 1 · 16, 2 · 8, 4 · 4 3. 17 1 · 17 4. 36 1 · 36, 2 · 18, 3 · 12, 4 · 9, 6 · 6 5. 23 1 · 23 Course 2

2 -4 Prime Factorization Problem of the Day Nicholas bikes every third day and skates every other day. Today is April 5, and Nicholas biked and skated. On what date will he both bike and skate? April 11 Course 2

2 -4 Prime Factorization Learn to find the prime factorizations of composite numbers. Course 2

2 -4 Prime Insert Factorization Lesson Title Here Vocabulary prime number composite number prime factorization Course 2

2 -4 Prime Factorization In June 1999, Nayan Hajratwala discovered the first known prime number with more than one million digits. The new prime number, 26, 972, 593 – 1, has 2, 098, 960 digits. A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. Three is a prime number because its only factors are 1 and 3. Course 2

2 -4 Prime Factorization A composite number is a whole number that has more than two factors. Six is a composite number because it has more than two factors— 1, 2, 3, and 6. The number 1 has exactly one factor and is neither prime nor composite. 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. Course 2

2 -4 Prime Factorization Additional Example 1 A: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. A. 24 24 8 · 3 4 · 2 · 3 Write 24 as the product of two factors. Continue factoring until all factors are prime. 2 · 2 · 3 The prime factorization of 24 is 2 · 2 · 3. Using exponents, you can write this as 23 · 3. Course 2

2 -4 Prime Factorization Additional Example B: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. B. 150 30 · 5 10 · 3 · 5 2 · 5 · 3 · 5 Write 150 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 150 is 2 · 3 · 5, or 2 · 3 · 5 2. Course 2

2 -4 Prime Insert Factorization Lesson Title Here Try This: Example 1 A Write the prime factorization of the number. A. 36 36 18 · 2 9 · 2 Write 36 as the product of two factors. Continue factoring until all factors are prime. 3 · 2 · 2 The prime factorization of 36 is 2 · 3 · 3. Using exponents, you can write this as 22 · 32. Course 2

2 -4 Prime Insert Factorization Lesson Title Here Try This: Example 1 B Write the prime factorization of the number. B. 90 90 45 · 2 9 · 5 · 2 3 · 5 · 2 Write 90 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 90 is 3 · 5 · 2, or 2 · 32 · 5. Course 2

2 -4 Prime Factorization You can also use a step diagram 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. The prime factors are the number are the prime numbers you divided by. Course 2

2 -4 Prime Factorization Additional Example 2 A: Using a Step Diagram to Find Prime Factorization Write the prime factorization of each number. A. 476 2 238 7 119 17 17 1 Divide 476 by 2. Write the quotient below 476. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 476 is 2 · 7 · 17, or 22 · 7 · 17. Course 2

2 -4 Prime Factorization Additional Example 2 B: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. B. 275 5 55 11 11 1 Divide 275 by 5. Write the quotient below 275. Stop when the quotient is 1. The prime factorization of 275 is 5 · 11, or 52 · 11. Course 2

2 -4 Prime Insert Factorization Lesson Title Here Try This: Example 2 A Write the prime factorization of each number. A. 324 2 162 3 81 3 27 3 9 3 3 1 The prime factorization 2 2 · 3 4. Course 2 Divide 324 by 2. Write the quotient below 324. Keep dividing by a prime number. Stop when the quotient is 1. of 324 is 2 · 3 · 3 · 3, or

2 -4 Prime Insert Factorization Lesson Title Here Try This: Example 2 B Write the prime factorization of the number. B. 325 5 65 13 13 1 Divide 325 by 5. Write the quotient below 325. Stop when the quotient is 1. The prime factorization of 325 is 5 · 13, or 52 · 13. Course 2

2 -4 Prime Factorization There is only one prime factorization for any given composite number. Example 2 A 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 2 238 7 119 17 17 1 7 476 2 68 2 34 17 17 1 The prime factorizations are 2 · 7 · 17 and 7 · 2 · 17, which are the same as 17 · 2 · 7. Course 2

2 -4 Prime Insert Factorization Lesson Title Here Lesson Quiz Use a factor tree to find the prime factorization. 33 1. 27 2. 36 22 · 3 2 3. 28 22 · 7 Use a step diagram to find the prime factorization. 4. 132 5. 52 6. 108 Course 2 22 · 3 · 11 22 · 13 22 · 3 3