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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.