Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2601:30 AM EDT
-02:30 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
May 0111:00 AM PDT
-12:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
25 May 2008, 11:56
Kudos
Bookmarks
How many zeros does 100! end with?
(anybody know a nifty way to do this, what if was how many zeros does 4500! end with?)
(anybody know a nifty way to do this, what if was how many zeros does 4500! end with?)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
25 May 2008, 12:07
Kudos
Bookmarks
one zero corresponds to 2*5. As we have 2 more often in n! than 5. So, we have to count 5.
4500!
(4500-5)/5+1=900
(4500-25)/25+1=180
(4500-125)/125+1=36
(4375-625)/625+1=7
(3125-3125)/3125+1=1
So 4500! has 900+180+36+7+1=1124 zeros
4500!
(4500-5)/5+1=900
(4500-25)/25+1=180
(4500-125)/125+1=36
(4375-625)/625+1=7
(3125-3125)/3125+1=1
So 4500! has 900+180+36+7+1=1124 zeros
Updated on: 13 Jul 2010, 13:12
Originally posted by TheGMATDoctor on 25 May 2008, 14:21.
Last edited by TheGMATDoctor on 13 Jul 2010, 13:12, edited 3 times in total.
Last edited by TheGMATDoctor on 13 Jul 2010, 13:12, edited 3 times in total.
Kudos
Bookmarks
We'll know the number of ending zeros of 100! by finding the largest power of 10 contained in 100!
Why? Because for example 1000= 10^3;so 1000 has 3 ending zeros.
900= 9*10^2; so 900 has 2 ending zeros.
Now to solve the problem, we first need to break down 10 into prime numbers. 10 = 2*5.
We then need to find how many 2s (call it x) and how many 5s (call it y) go in 100!
Once we do that, we'll take the lower number between x and y.
Clearly, there will be more 2s than 5s in 100!; so let's save time by focusing on y (the number of 5).
Let's do it:
Divide 100 by 5 and the resulting quotient by 5 repeatedly until the quotient of the division is less than 5, which is the divisor, and you stop.
We only write out and take the quotients in the divisions.
100/5 = 20; 20/5= 4. Stop! since 4 is less than 5.
Let's now add all the quotients: y= 20 + 4 = 24.
24 is the largest power of 5 in 100!
24 is also the largest power of 10 contained in 100!
100! has 24 ending zeros!
That's all folks!
Asan Azu, The GMAT Doctor.
Asan is a very experienced GMAT teacher and tutor that can be reached at https://www.GMATLounge.com
For 4500, the same methodology applies. Remember that we only take the quotients in the successive divisions by 5.
4500/5 = 900; 900/5 = 180; 180/5 = 36; 36/5 = 7; 7/5 = 1; Stop! since 1 is less than 5.
Now add the quotients : y= 900+180+36+7+7 = 1124.
1124 is the largest power of 10 contained in 4500!
4500! has 1124 ending zeros.
Done.
Why? Because for example 1000= 10^3;so 1000 has 3 ending zeros.
900= 9*10^2; so 900 has 2 ending zeros.
Now to solve the problem, we first need to break down 10 into prime numbers. 10 = 2*5.
We then need to find how many 2s (call it x) and how many 5s (call it y) go in 100!
Once we do that, we'll take the lower number between x and y.
Clearly, there will be more 2s than 5s in 100!; so let's save time by focusing on y (the number of 5).
Let's do it:
Divide 100 by 5 and the resulting quotient by 5 repeatedly until the quotient of the division is less than 5, which is the divisor, and you stop.
We only write out and take the quotients in the divisions.
100/5 = 20; 20/5= 4. Stop! since 4 is less than 5.
Let's now add all the quotients: y= 20 + 4 = 24.
24 is the largest power of 5 in 100!
24 is also the largest power of 10 contained in 100!
100! has 24 ending zeros!
That's all folks!
Asan Azu, The GMAT Doctor.
Asan is a very experienced GMAT teacher and tutor that can be reached at https://www.GMATLounge.com
For 4500, the same methodology applies. Remember that we only take the quotients in the successive divisions by 5.
4500/5 = 900; 900/5 = 180; 180/5 = 36; 36/5 = 7; 7/5 = 1; Stop! since 1 is less than 5.
Now add the quotients : y= 900+180+36+7+7 = 1124.
1124 is the largest power of 10 contained in 4500!
4500! has 1124 ending zeros.
Done.
Quote:
approach:
