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## Prime Factorization

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**Prime Factorization**Lesson 4.2**A Product of Primes**• Every composite number can be expressed as a product of prime numbers. • This is called prime factorization.**Example**• 15 is a composite number. • It can be expressed as a product of primes: 3 x 5**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.**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…**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.**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.**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**Another Example**420 2 x 210 2 x 105 22 x 3 x 5 x 7 3 x 35 5 x 7**Try this on your own:**54 Answer: 2 x 33