Prime Factorization

1. Prime Factorization Lesson 4.2

2. A Product of Primes • Every composite number can be expressed as a product of prime numbers. • This is called prime factorization.

3. Example • 15 is a composite number. • It can be expressed as a product of primes: 3 x 5

4. To find the prime factorization: • Divide the number by the first prime number possible. • Circle the prime number, and continue with the other factor. • Divide the new factor by a prime number. • Continue this process until the only numbers you have left are prime numbers.

5. Remember the Prime Number List: • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97…

6. Example: Prime Factorization of 100. 100 100 ÷ 2 = 50. Two is the first prime number that goes into 100. Now we deal with the 50. Divide it by 2 to get the next factors. 2 is a prime number, so we are done with it. 2 X 50 25 is not divisible by the first prime, 2. The next prime, 3, does not work either. We must divide by 5 to get a factor. 2 X 25 5 x 5 Both numbers are prime, leaving us with all primes.

7. What’s the Answer? • Now, we just list our factors with multiplication signs between them. Use the circled prime numbers. • 2 x 2 x 5 x 5 • We have listed 100 as a product of prime numbers.

8. Exponent Form • We have just listed our prime factorization for 100 as being 2 x 2 x 5 x 5. This is repeated multiplication. Repeated multiplication can be expressed with exponents. • Our prime numbers are our bases. The number of times the prime number is written is the exponent. • 2 x 2 can be expressed in exponent form: 22 • 5 x 5 can be expressed as 52 • Put it together, and 2 x 2 x 5 x 5 is more simply put as 22 x 52

9. Another Example 420 2 x 210 2 x 105 22 x 3 x 5 x 7 3 x 35 5 x 7

10. Try this on your own: 54 Answer: 2 x 33

11. Homework Time!