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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 ____________________________________________________ © 2010, James A. Sellers