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

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

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

Course Prime Factorization 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. The first prime number is 2 The first several prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Course 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.

Tell whether each number is prime or composite. Additional Example 1: Identifying Prime and Composite Numbers Course Prime Factorization A is prime. The factors of 11 are 1 and 11. B is composite. The factors of 16 are 1, 2, 4, 8, and 16.

Tell whether each number is prime or composite. Check It Out: Example 1 Course Prime Factorization A is composite. The factors of 14 are 1, 2, 7, and 14. B. 7 7 is prime. The factors of 7 are 1 and 7.

Course Prime Factorization 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 Prime Factorization You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. Writing Math

Write the prime factorization of each number. Additional Example 2A: Using a Factor Tree to Find Prime Factorization Course Prime Factorization 24 8 · 3 4 · 2 2 · 2 Write 24 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 24 is 2 · 2 · 2 · 3 or 2 3 · 3.

Write the prime factorization of each number. Additional Example 2B: Using a Factor Tree to Find Prime Factorization Course Prime Factorization · 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 · 5, or 2 · 3 · 5 2.

Check It Out: Example 2A Insert Lesson Title Here Course Prime Factorization Write the prime factorization of each number · 2 9 · 2 · 2 3 · 3 · 2 · 2 Write 36 as the product of two factors. Continue factoring until all factors are prime. The prime factorization of 36 is 2 · 2 · 3 · 3 or 2 2 · 3 2.

Check It Out: Example 2B Insert Lesson Title Here Course Prime Factorization Write the prime factorization of the number · 2 9 · 5 · 2 3 · 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 · 3 · 5 · 2, or 2 · 3 2 · 5.

Course 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.

Write the prime factorization of each number. Additional Example 3A: Using a Step Diagram to Find Prime Factorization Course Prime Factorization 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 · 2 · 7 · 17, or 2 2 · 7 · 17.

Write the prime factorization of the number. Additional Example 3B: Using a Step Diagram to Find Prime Factorization Course Prime Factorization Divide 275 by 5. Write the quotient below 275. Stop when the quotient is 1. The prime factorization of 275 is 5 · 5 · 11, or 5 2 · 11.

Check It Out: Example 3A Insert Lesson Title Here Course Prime Factorization Write the prime factorization of each number Divide 324 by 2. Write the quotient below 324. Keep dividing by a prime number. Stop when the quotient is 1. The prime factorization of 324 is 2 · 2 · 3 · 3 · 3 · 3, or 2 2 ·

Check It Out: Example 3B Insert Lesson Title Here Course Prime Factorization Write the prime factorization of the number Divide 325 by 5. Write the quotient below 325. Stop when the quotient is 1. The prime factorization of 325 is 5 · 5 · 13, or 5 2 · 13.

Lesson Quiz: Part I Tell whether each number is prime or composite composite prime Insert Lesson Title Here composite Course Prime Factorization

Lesson Quiz: Part II Write the prime factorization of each number · Insert Lesson Title Here 2 2 · · 3 · 11 Course Prime Factorization 2 2 · · 3 3