1. What are factors? What makes a number prime or composite?

2. Some things to remember before we start: A sum is the answer to an addition problem. A difference is the answer to a subtraction problem. A product is the answer to a multiplication problem. A quotient is the answer to a division problem. A whole number is an integer, or a “counting number”. 13 is a whole number. 13 ½ is not.

3. Factors A factor is one of two or more whole numbers that are multiplied to get a product. For example, 3 and 8 are both factors of 24 because 3 times 8 is 24. Can you list all the factors of 24? Can you list all the factor pairs of 18?

4. Factors (cont.) Another name for a factor is a divisor. There are rules that can help you decide if a number is divisible by certain numbers. These are called divisibility rules. Here are a few:file://localhost/Users/thara valdes/Desktop/Back to School:First Week/Some Divisibility Rules.docxfile://localhost/Users/thara valdes/Desktop/Back to School:First Week/Some Divisibility Rules.docx Is 105 divisible by 2? By 3? By 5? By 10? Is 60 divisible by 2? By 3? By 5? By 10?

5. Prime Numbers If a number only has two factors, 1 and the number itself, the number is a prime number. Is 13 prime? Explain. Is 9 prime? Explain. Why isn’t 1 a prime number? Here is a list of the first 1000 prime numbers: http://primes.utm.edu/lists/small/1000.txt

6. Composite Numbers If a number has more than two factors, it is a composite number. Explain why 14 is a composite number.

7. Proper Factors The proper factors of a number are all of the factors of the number, EXCEPT for the number itself. Ex: The proper factors of 12 are 1, 2, 3, 4, and 6. What are the proper factors of 20? The sum of the proper factors of a number may be greater than, less than, or equal to the number. This idea is used to classify numbers as abundant, deficient, or perfect.

8. Proper factors (cont.) A number is abundant if the sum of all its proper factors is greater than the number itself. 24 is abundant because its proper factors, 1, 2, 3, 4, 6, 8, and 12 add to 36, which is greater than 24. A number is deficient if the sum of its proper factors is less than the number itself. 14 is deficient because its proper factors, 1, 2, and 7 add to 10, which is less than 14. ALL prime numbers are deficient. A number is perfect if the sum of its proper factors is equal to the number itself. 6 is a perfect number because its proper factors, 1, 2, and 3 add up to 6.