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## Prime Factorization

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**A prime numberis 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. What are the rest of the prime numbers? 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.**A. 11 B. 16 The factors of 11 are 1 and 11. The factors of 16 are 1, 2, 4, 8, and 16. 11 is prime. 16 is composite.**Tell whether each number is prime or composite.**C. 14 D. 7 The factors of 14 are 1, 2, 7, and 14. The factors of 7 are 1 and 7. 7 is prime. 14 is composite.**Writing Math**You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor. 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.**Write the prime factorization of each number.**24 Write 24 as the product of two factors. 8 · 3 4 · 2 Continue factoring until all factors are prime. 2 · 2 The prime factorization of 24 is 2 · 2 · 2 · 3 or 23 · 3.**Write the prime factorization of each number.**150 Write 150 as the product of two factors. 30 · 5 Continue factoring until all factors are prime. 10 · 3 2 · 5 The prime factorization of 150 is 2 · 3 · 5 · 5, or 2 · 3 · 52.**Write the prime factorization of each number.**36 Write 36 as the product of two factors. 18 · 2 Continue factoring until all factors are prime. 9 · 2 3 · 3 The prime factorization of 36 is 2 · 2 · 3 · 3 or 22 · 32.**Write the prime factorization of the number.**90 Write 90 as the product of two factors. 45 · 2 Continue factoring until all factors are prime. 9 · 5 3 · 3 The prime factorization of 90 is 3 · 3 · 5 · 2, or 2 · 32 · 5.**ASSIGNMENT**• WS 33 You are A-MAZE-ING!**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.**When you get to 1 you are finished**Repeated Division Start by dividing by the smallest prime number. 40 2 20 2 Keep using 2 until it will not work anymore. 2 10 5 5 1 2 x 2 x 2 x 5 = 2³ x 5**When you get to 1 you are finished**Let’s try another one… Start by dividing by the smallest prime number. 42 2 3 2 will no longer work so you need to try the next prime number…3! 21 7 7 1 2 x 3 x 7**Now you try!**2 18 2 28 3 9 2 14 3 3 7 7 1 1 2 x 32 22 x 7**Write the prime factorization of the number.**325 Divide 325 by 5. Write the quotient below 325. 325 5 65 5 13 13 Stop when the quotient is 1. 1 The prime factorization of 325 is 5 · 5 · 13, or 52 · 13.**Write the prime factorization of the number.**275 Divide 275 by 5. Write the quotient below 275. 275 5 55 5 11 11 Stop when the quotient is 1. 1 The prime factorization of 275 is 5 · 5 · 11, or 52 · 11.**Write the prime factorization of each number.**476 Divide 476 by 2. Write the quotient below 476. 476 2 238 2 Keep dividing by a prime number. 119 7 17 17 1 Stop when the quotient is 1. The prime factorization of 476 is 2 · 2 · 7 · 17, or 22 · 7 · 17.**There is only one prime factorization for any given**composite number. The last example began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 476 476 2 7 238 68 2 2 119 34 7 2 17 17 17 17 1 1 The prime factorizations are 2 · 2 · 7 · 17 and 7 · 2 · 2 · 17, which are the same as 17 · 2 · 2 · 7.