rimeFactorization-TheUniversityofChicago素因子分解-芝加哥大学.ppt

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 2 X 50 100 2 = 50. Two is the first prime number that goes into 100. 2 is a prime number, so we are done with it. Now we deal with the 50. Divide it by 2 to get the next factors. 2 X 25 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. 5 x 5 Both numbers are prime, leaving us with all primes. Whats 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: 2 2 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