## Rangpur Secondary 2011/3

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
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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?
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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\$
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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.
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Nur Muhammad Shafiullah | Mahi

Mahfuz Sobhan
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### Re: Rangpur Secondary 2011/3

thanks mahi bhai.