Download Prime Factorization

Academic Learning Center
Math Handout
Prime Factorization
Prime Number – A number whose only factors are 1 and itself.
Prime Factorization – Factoring a number into numbers that are all prime.
Ex. 1
18
18 factors into 9 and 2
9
2
9 factors into 3 and 3
3
3
(Always circle the prime numbers in
your tree)
So the Prime Factorization of 18 is
2 x 3 x 3 (Always sort the prime numbers
from smallest to largest)
Combine all common factors into one
Exponent term:
2 x 3 x 3 = 2 × 32
Note: There is more than one way to create your factor tree. But your final
prime factorization will always be the same.
18
18 factors into 6 and 3
6
3
6 factors into 2 and 3
2
3
Note that the final Prime Factorization
Comes out to be the same as before.
2 x 3 x 3 = 2 × 32
Academic Learning Center ~ Central Piedmont Community College ~ Central High Room 103 ~ 704-330-6474
Ex. 2
20
5
4
2
2
Ex. 3
42
6
3
7
2
2x3x7
Ex. 4
45
9
3
5
3 x 3 x 5 = 32 × 5
3
Ex. 5
50
5
10
5
Ex. 6
2
2 x 5 x 5 = 2 × 52
24
6
3
2 x 2 x 5 = 22 × 5
4
2 2
2
3
2 x 2 x 2 x 3 = 2 ×3
Academic Learning Center ~ Central Piedmont Community College ~ Central High Room 103 ~ 704-330-6474
Ex. 7
16
4
2
4
2 2
Ex. 8
54
9
3
4
2x2x2x2= 2
2
6
3 2
3
2 x 3 x 3 x 3 = 2×3
3
Ex. 9
7
Prime
Ex. 10
7
60
6
2
10
3 2
5
2 x 2 x 3 x 5 = 22 × 3× 5
Academic Learning Center ~ Central Piedmont Community College ~ Central High Room 103 ~ 704-330-6474