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Rangpur Secondary 2011/3

Posted: Wed Feb 02, 2011 6:48 pm
by Moon
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?

Re: Rangpur Secondary 2011/3

Posted: Wed Feb 02, 2011 7:29 pm
by Tahmid Hasan
$$2048=2^{11}=2^62^5=64*32$$
so the difference is 32.

Re: Rangpur Secondary 2011/3

Posted: Thu Feb 03, 2011 8:25 pm
by *Mahi*
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$2^11$

Re: Rangpur Secondary 2011/3

Posted: Thu Feb 03, 2011 9:26 pm
by Tahmid Hasan
sry didn't notice that :mrgreen:

Re: Rangpur Secondary 2011/3

Posted: Mon May 11, 2015 1:22 pm
by Mahfuz Sobhan
how will i understand that 2048 in equal to 2 to the power 11 without any calculator?

Re: Rangpur Secondary 2011/3

Posted: Mon May 11, 2015 7:45 pm
by *Mahi*
Try to factorize $2048$ - it should be straightforward after the question.

Re: Rangpur Secondary 2011/3

Posted: Mon May 11, 2015 9:26 pm
by Mahfuz Sobhan
thanks mahi bhai.