4. n! (read "n factorial") is the product of the first n positive integers, that is 2! = 2 1, 3! = 3-2 1, etc. (a) How many zeroes are in the rightmost places (digits) of the large number 17! ? (b) Find the smallest natural number n such that n! ends in exactly 37 zeroes.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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4. n! (read "n factorial") is the product of the first n positive integers, that is 2! = 2 1, 3! = 3 2 1,
etc.
(a) How many zeroes are in the rightmost places (digits) of the large number 17! ?
(b) Find the smallest natural number n such that n! ends in exactly 37 zeroes.
Transcribed Image Text:4. n! (read "n factorial") is the product of the first n positive integers, that is 2! = 2 1, 3! = 3 2 1, etc. (a) How many zeroes are in the rightmost places (digits) of the large number 17! ? (b) Find the smallest natural number n such that n! ends in exactly 37 zeroes.
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