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Factors Terminology: 3 4 =12 The number’s 3 and 4 are called Factors. The result, 12, is called the product. We say that 3 and 4 are factors of 12. However, the number 12 has other factors: 2 6 = 12 1 12= 12 So the complete list of factors for 12 is 1, 2, 3, 4, 6, and 12. Another way of stating what factor are is: “Numbers that divide evenly into a given number”. 1, 2, 3, 4, 6, and 12 all divide evenly into 12. The number 5 is not a factor because it does not divide evenly into 12 (there is a remainder). Example 2. List all the factors of 24. Check sequentially the numbers 1, 2, 3, and so on, to see if we can form any factorizations. 24 1 24 2 12 3 8 4 6 Answer: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Your Turn Problem #2 List all the factors of 48. Answer: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

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**A prime number is a whole number greater than 1 that is only divisible by itself and 1.**

A prime number therefore has only two factors—itself and 1. The Prime Numbers Are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, ... Note: Each of these numbers is only divisible by itself and 1. Note: Because a prime number must be greater than 1, this makes the first prime number, by definition 2 Prime Numbers A composite numbers is a number that is divisible by other numbers besides itself and 1. A composite number has more than two factors. The Composite Numbers Are: (all whole numbers that are not prime): 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, ... Composite Numbers It is important to be able to determine whether a number is prime of composite because it will be a necessary part of the prime factorization process. The prime factorization process will be necessary for concepts such as reducing, adding and subtracting fractions. Determining Prime Numbers Next Slide

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**Procedure: To determine if a number if a number is prime of composite:**

Step 1: Use the tests of divisibility to determine if it is divisible by 2, 3, or 5. If none of these work, Step 2: Try to divide the number by the prime numbers beginning with 7, 11, 13, etc. Step 3: Continue this process until the prime number you are dividing is such that when it is multiplied by itself, the product is larger than the number being tested. To summarize: In using the list of prime numbers, if you cannot find one that is divisible into the number being tested, then the number is prime. If you can find a prime number or any other number that is divisible into the number, then the number is composite. Example 3: Determine whether the following are prime or composite: a) 87, b) 97, and c) 539 Solution: a) 87 is composite because it is divisible by 3 (add its digits). b) 97 is not divisible by 2, 3, or 5 (divisibility tests do not work), & it is not divisible by 7 (when you divide it gives a remainder). The next prime number, 11, is not tested because when multiplied by itself, the product, 121, is larger than 97. Answers: 87: composite, 97: prime, 539: composite c) 539 is not divisible by 2, 3, or 5 (divisibility tests do not work), but when we divide by the next prime, 7, we get a quotient with no remainder. Your Turn Problem #3 Determine whether the following are prime or composite: a) 91, b) 57, and c) 103 Answers: a) composite b) composite c) prime

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