Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education

Chapter 4 - Section 4.3 - Primes and Greatest Common Divisors - Exercises: 5

Answer

$10!=7⋅5^2⋅3^3⋅2^7$

Work Step by Step

To find the prime factorization of 10!, it helps to first write out what that means. 10!=10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1. Then we begin to rearrange these numbers from the smallest factor first. $10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1 =5⋅2⋅3^2⋅2^3⋅7⋅2⋅3⋅5⋅2^2⋅3⋅2⋅1=7⋅5^2⋅3^3⋅2^7$

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