## Rangpur Secondary 2011/3

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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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.
Moon
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### 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?
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

learn how to write equations, and don't forget to read Forum Guide and Rules.

Tahmid Hasan
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### Re: Rangpur Secondary 2011/3

\$\$2048=2^{11}=2^62^5=64*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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*Mahi*
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### Re: Rangpur Secondary 2011/3

Tahmid Hasan wrote:\$\$2048=2^11=2^62^5=64*32\$\$
so the difference is 32.
Tahmid-please write \$2^{11}\$ as 2^{11} in latex,because if you write 2^11 in latex it will be\$2^11\$

Use \$L^AT_EX\$, It makes our work a lot easier!

Tahmid Hasan
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### Re: Rangpur Secondary 2011/3

sry didn't notice that
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Mahfuz Sobhan
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### Re: Rangpur Secondary 2011/3

how will i understand that 2048 in equal to 2 to the power 11 without any calculator?

*Mahi*
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### Re: Rangpur Secondary 2011/3

Try to factorize \$2048\$ - it should be straightforward after the question.