# Fundamental Theorem of Arithmetic - Personal.psu.edu

```MATH 035
Penn State University
Dr. James Sellers
Handout: Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic
Every integer greater than 1 can be written in a unique way as the product of prime factors (up
to the order in which the primes are written).
Exercises:
Rewrite each of the following products using exponential notation.
2 &times; 2 &times; 2 &times; 2 &times; 2 &times; 2 ____________________________________________________
3 &times; 3 &times; 3 &times; 5 &times; 5 _______________________________________________________
2 &times; 7 &times; 2 &times; 7 &times; 7 &times; 2 &times; 2 __________________________________________________
5 &times; 5 &times; 3 &times; 3 &times; 3 &times; 2 _____________________________________________________
7 &times;11&times; 11&times; 13 &times; 17 &times; 17 _________________________________________________
Expand the following and write them as one number.
25 _________________________________________
34 &times; 52 ______________________________________
5 &times; 7 2 &times; 313 ___________________________________
210 &times; 510 _____________________________________
Find the prime factorizations for each of the following. (Write the prime factors in order from
smallest to largest as you read left-to-right.)
500
____________________________________________________
726
____________________________________________________
1287
____________________________________________________
2432
____________________________________________________
4096
____________________________________________________
10000 ____________________________________________________
12121 ____________________________________________________
7575
____________________________________________________
5432
____________________________________________________
4444
____________________________________________________
&copy; 2010, James A. Sellers
```