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 × 2 × 2 × 2 × 2 × 2 ____________________________________________________
3 × 3 × 3 × 5 × 5 _______________________________________________________
2 × 7 × 2 × 7 × 7 × 2 × 2 __________________________________________________
5 × 5 × 3 × 3 × 3 × 2 _____________________________________________________
7 ×11× 11× 13 × 17 × 17 _________________________________________________
Expand the following and write them as one number.
25 _________________________________________
34 × 52 ______________________________________
5 × 7 2 × 313 ___________________________________
210 × 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
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© 2010, James A. Sellers