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Prime Factorization Notes Problem Definitions: exponents - small raised numbers that tell you how many times a factor is repeated Factor Trees are used to keep track of all the prime factors in a number. Look at each of the factor trees for the number 100. 100 2 2 2 X X X5 25 0 100 50 X X 5 X 4 2 X 100 25 10 X 5 2 X 2 X5 X 2 X 5 X2 10 X 5 2 Notice that the bottom row of each tree contains the same factors, although the order of the factors is different. All three trees indicate that the longest factorization for 100 is 2 x 2 x 5 x 5. Try the number 600. Are there other ways to list the factors? 600 4 2 X 100 X X 25 X 6 2 X 3 0 2 X5 X 5 X 2 X 3 You can use a shortcut to write 2 x 2 x 5 x 5 x 2 x 3. In this shortcut, the string is written: 23 x 3 x 5 2 The small raised numbers are exponents and tell us how many times the factor is repeated.