1. Prime Factorization Notes 9/8/10 Composite Number- a whole number greater than 1 with more than two factors. Prime Number – A whole number with exactly two factors, 1 and the number itself. 0 and 1 are neither prime nor composite. Prime Factorization: The longest factor string for a number, composed entirely of prime numbers. Ex: the prime factorization of 12 is 2 x 2 x 3 or 2^2 x 3. Exponent: The small raised number that tells how many times a factor is used. Ex: 5^3 means 5 x 5 x 5.

2. Prime Factorization Notes 1.Using your divisibility rules, think about what prime numbers will go into the number. 2. Continue dividing the number by prime numbers until all you have left is prime numbers. 3. Write your answer using exponents *You cannot use the number one for this! * Remember the prime numbers 2, 3, 5, 7, 11, 13*

3. Exponents An exponent is used to tell you how many times a base number is to be listed and used as a factor. –Ex. 3 4 = 3x3x3x3 = ___ –Ex. 5 3 = 5x5x5 = ___ –Try this one: 2 6 = ____________ = _____ Exponents can be used to express prime factorization in a more concise manner. Ex. 2x2x3x5x5 would be written 2 2 x3x5 2

4. Making a Factor Tree 1.Put the number at the top. 2. Break the number down into a prime number times another factor and branch out. 3. Circle all prime numbers as you go! 4. Continue breaking it down until all you have left is prime numbers. 5. Use exponents if you can to write the prime number factors.

5. Using the Ladder Method 1. Put the number at the top. 2. Draw a ladder underneath it and divide it by a prime number. Write the new number underneath the sled. 3. All prime numbers should be down the left side. 4. Continue breaking it down until all you have left is a prime number at the bottom. 5. The numbers on the outside of the ladders are the prime factorization.

6. EXAMPLE of both methods on the same number: Factor TreeDivision Ladder 200200

7. YOU TRY SOME PRIME FACTORIZATION Factor TreeDivision Ladder 9090 120120