Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Imagine the product of $20^{50}$ and $50^{20}$ written as an integer in standard form. how many zeros will be found at the end of this number?

share|improve this question

closed as off-topic by Weapon of Choice, T. Bongers, Gina, Adam Hughes, Tomás Aug 1 at 0:42

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Weapon of Choice, Community, Gina, Adam Hughes, Tomás
If this question can be reworded to fit the rules in the help center, please edit the question.

    
Do you mean 20^{50} and 50^{20}? –  Amzoti Dec 16 '12 at 18:41
2  
What have you tried? A zero at the end of this product comes from a factor of $10=2\cdot 5$ in it. So, how many $10$ can you produce? –  lhf Dec 16 '12 at 18:42
    
This question has nothing to do with either integer-lattices or integer-programming so I've retagged it. (Of course, if you can think of more appropriate tags, feel free to change the tags I've chosen.) –  Martin Sleziak Dec 16 '12 at 18:48

1 Answer 1

HINT: $20^{50}\cdot50^{20}=\left(2\cdot10\right)^{50}\left(5\cdot10\right)^{20}=2^{50}\cdot10^{50}\cdot5^{20}\cdot10^{20}=2^{50}\cdot5^{20}\cdot10^{50+20}$. How many zeroes will you get from $10^{50+20}$? How many more from $2^{50}\cdot5^{20}$?

share|improve this answer
    
Actually, how many (for $2^{50} \cdot 5^{50}$)? –  Shahar May 12 at 3:58

Not the answer you're looking for? Browse other questions tagged or ask your own question.