Rangpur Secondary 2011/3
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Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Rangpur Secondary 2011/3
Problem 3:
If $2048$ is written as a product of two positive integers whose difference is as small as possible, then what is the difference?
If $2048$ is written as a product of two positive integers whose difference is as small as possible, then what is the difference?
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 Tahmid Hasan
 Posts: 665
 Joined: Thu Dec 09, 2010 5:34 pm
 Location: Khulna,Bangladesh.
Re: Rangpur Secondary 2011/3
$$2048=2^{11}=2^62^5=64*32$$
so the difference is 32.
so the difference is 32.
Last edited by Tahmid Hasan on Thu Feb 03, 2011 9:25 pm, edited 1 time in total.
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Re: Rangpur Secondary 2011/3
Tahmidplease write $2^{11}$ as 2^{11} in latex,because if you write 2^11 in latex it will be$2^11$Tahmid Hasan wrote:$$2048=2^11=2^62^5=64*32$$
so the difference is 32.
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Nur Muhammad Shafiullah  Mahi
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 Tahmid Hasan
 Posts: 665
 Joined: Thu Dec 09, 2010 5:34 pm
 Location: Khulna,Bangladesh.

 Posts: 25
 Joined: Sat Feb 07, 2015 5:40 pm
Re: Rangpur Secondary 2011/3
how will i understand that 2048 in equal to 2 to the power 11 without any calculator?
Re: Rangpur Secondary 2011/3
Try to factorize $2048$  it should be straightforward after the question.
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah  Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah  Mahi

 Posts: 25
 Joined: Sat Feb 07, 2015 5:40 pm
Re: Rangpur Secondary 2011/3
thanks mahi bhai.