## Discrete Mathematics and Its Applications, Seventh Edition

$10!=7⋅5^2⋅3^3⋅2^7$
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. $10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1 =5⋅2⋅3^2⋅2^3⋅7⋅2⋅3⋅5⋅2^2⋅3⋅2⋅1=7⋅5^2⋅3^3⋅2^7$