3 1 Prime Factorization California Standards Preparation for

3 -1 Prime Factorization Vocabulary prime number A whole number greater than 1 that

3 -1 Prime Factorization A prime number is a whole number greater than 1

3 -1 Prime Factorization Example 1: Identifying Prime and Composite Numbers Tell whether each

3 -1 Prime Factorization A composite number can be written as the product of

3 -1 Prime Factorization Writing Math You can write prime factorization by using exponents.

3 -1 Prime Factorization Example 2 A: Using a Factor Tree to Find Prime

3 -1 Prime Factorization Example 2 B: Using a Factor Tree to Find Prime

3 -1 Prime Factorization You can also use a step diagram to find the

3 -1 Prime Factorization Example 3 A: Using a Step Diagram to Find Prime

3 -1 Prime Factorization Example 3 B: Using a Step Diagram to Find Prime

3 -1 Prime Factorization Check It Out! Example 1 Tell whether the number is

3 -1 Prime Factorization Check It Out! Example 2 Write the prime factorization of

3 -1 Prime Factorization Check It Out! Example 3 Write the prime factorization of

3 -1 Prime Factorization There is only one prime factorization for any given composite

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3 -1 Prime Factorization California Standards Preparation for NS 2. 4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e. g. to find a common denominator to add two fractions or to find the reduced form for a fraction). Holt CA Course 1

3 -1 Prime Factorization Vocabulary prime number A whole number greater than 1 that has exactly two positive factors, itself and 1. composite number A whole number that has more than two positive factors. prime factorization A number written as the product of its prime factors. Holt CA Course 1

3 -1 Prime Factorization A prime number is a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3. A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors— 1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite. Holt CA Course 1

3 -1 Prime Factorization Example 1: Identifying Prime and Composite Numbers Tell whether each number is prime or composite. A. 11 The positive factors of 11 are 1 and 11. B. 16 The positive factors of 16 are 1, 2, 4, 8, and 16. So 11 is prime. So 16 is composite. Holt CA Course 1

3 -1 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. Holt CA Course 1

3 -1 Prime Factorization Writing Math You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. Holt CA Course 1

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

3 -1 Prime Factorization Example 2 B: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. 150 30 5 10 3 5 2 5 3 5 Write 150 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 150 is 2 3 5 5, or 2 3 5 2. Holt CA Course 1

3 -1 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. Holt CA Course 1

3 -1 Prime Factorization Example 3 A: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. 476 2 238 7 119 17 17 1 Divide 476 by 2. Write the quotient below 476. Keep dividing by a prime factor. Stop when the quotient is 1. The prime factorization of 476 is 2 2 7 17, or 22 7 17. Holt CA Course 1

3 -1 Prime Factorization Example 3 B: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. 275 5 55 11 11 1 Divide 275 by 5. Write the quotient below 275. Keep dividing by a prime factor. Stop when the quotient is 1. The prime factorization of 275 is 5 5 11, or 52 11. Holt CA Course 1

3 -1 Prime Factorization Check It Out! Example 1 Tell whether the number is prime or composite. 14 The positive factors of 14 are 1, 2, 7, and 14. 14 is composite. Holt CA Course 1

3 -1 Prime Factorization Check It Out! Example 2 Write the prime factorization of the number. 90 90 45 2 9 5 2 3 3 5 2 Write 90 as the product of two positive factors. Continue factoring until all factors are prime. The prime factorization of 90 is 3 3 5 2, or 2 32 5. Holt CA Course 1

3 -1 Prime Factorization Check It Out! Example 3 Write the prime factorization of the number. 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 5 13, or 52 13. Holt CA Course 1

3 -1 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 2 7 17 and 7 2 2 17, which are the same as 17 2 2 7. Holt CA Course 1