1. In the Real World Dancers A dance teacher is planning a dance for a show. The dancers will be arranged in rows with the same number of dancers in each row. Can a group of 12 dancers or a group of 14 dancers be arranged in more ways? Prime Factorization 5 1.

2. A group of 12 dancers can be arranged in more ways than a group of 14 dancers, because 12 has more factors than 14. Finding Factors EXAMPLE 1 To answer the previous question, list all the factors of 12 and 14 by writing each number as a product of two numbers in as many ways as possible. 14: 1  14 2  7 7  2 The factors of 12 are: The factors of 14 are: 12: 1  12 2  6 3  4 4  3 1,3,4,6, and 12. 2, 1,2,7, and 14. ANSWER Prime Factorization 5 1. Stop when a pair of factors repeat.

3. NOTE BOOK Divisibility Rules for 2, 3, 5, 6, 9, and 10 A whole number is divisible by: 2 if the number is even. 5 if it ends with 5 or 0. 6 if it is even and is divisible by 3. 10 if it ends with 0. Divisibility A number is divisible by another number if that other number is a factor of the first. Divisibility rules can help you find factors. Prime Factorization 5 1. 9 if the sum of its digits is divisible by 9. 3 if the sum of its digits is divisible by 3.

4. Using Divisibility Rules EXAMPLE 2 Test 150 for divisibility by 2, 3, 5, 6, 9, and 10. 150 is even, 1 + 5 + 0 = 6, 150 ends with 0, 150 is even and divisible by 3, 150 is divisible by 2, 3, 5, 6 and 10, but not by 9. so it is divisible by 2. So, 150 is divisible by 3, but not divisible by 9. so it is divisible by 5 and by 10. so it is divisible by 6. ANSWER Prime Factorization 5 1. and 6 is divisible by 3, but not 9.

5. Prime Factorization 5 1. Primes and Composites A prime number is a whole number greater than 1 whose only factors are 1 and itself. A composite number is a whole number greater than 1 that has factors other than 1 and itself. The number 1 is neither prime nor composite.

6. Classifying as Prime or Composite Tell whether the number is prime or composite. 51 59 SOLUTION List the factors of 51: List the factors of 59: The number 59 is prime. Its only factors are 1 and itself. 1,1, The number 51 is composite. It has factors other than 1 and itself. EXAMPLE 3 1,1,3,3,17,51.59. ANSWER Prime Factorization 5 1. SOLUTION

7. Prime Factorization 5 1. Prime Factorization Writing the prime factorization of a number means writing the number as the product of prime numbers. You can use a diagram called a factor tree to write a factorization of a number. To write the prime factorization, continue factoring until only prime factors appear in the product.

8. Writing a Prime Factorization Write the prime factorization of 180. 180 1810  22335  2925  The prime factorization of 180 is 2 2  3 2  5. Use multiplication to check your answer. C HECK 2 2  3 2  5 = 4  9  5 = 180 EXAMPLE 4 Write the original number. Factor 180 as 10 times 18. Factor 10 and 18. Factor 9. ANSWER Prime Factorization 5 1.