ক্ষুদ্রতম সংখ্যা

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nisha
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ক্ষুদ্রতম সংখ্যা

Unread post by nisha » Mon Dec 12, 2011 9:08 pm

সবচেয়ে ক্ষুদ্রতম সংখ্যা নির্ণয় কর যাকে মোট 24 টি সংখ্যা দিয়ে নিঃশেষে ভাগ করা যায়।

jhal_muri
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by jhal_muri » Tue Dec 13, 2011 12:29 am

if u mean positive integer,then it is 24!

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Re: ক্ষুদ্রতম সংখ্যা

Unread post by nafistiham » Tue Dec 13, 2011 1:01 am

my smallest answer till now is $420$ ;)
the divisors are $1,2,3,4,5,84,6,7,10,12,14,15,20,21,28,30,35,42,60,70,105,70,210,420$
there are $26$ divisors
but, i think there is a smaller number. :?
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as-if
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by as-if » Tue Dec 13, 2011 1:50 am

ans is 420

jhal_muri
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by jhal_muri » Tue Dec 13, 2011 1:51 am

i have got the exact answer:-)it is 360 whose prime factorization is 2^3*3^2*5 which ensures its minimality.

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sm.joty
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by sm.joty » Tue Dec 13, 2011 3:05 pm

Yes, the right answer is $360$. Because 2,3,5 are the lowest prime numbers. Now use Divisor Function
If have the book Theory Of Numbers ---- by John e couri and Andrew adlar then see the book. Or without having book you can see this link. I think this is also useful for you.
http://mathschallenge.net/library/numbe ... f_divisors
:D
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by Prosenjit Basak » Tue Dec 18, 2012 11:59 am

I admit that the right ans is 360.But it can be more less like -360.It also have 24 divisors.Isn't it correct. :D Give me advice if I am wrong
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SANZEED
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Re: ক্ষুদ্রতম সংখ্যা

Unread post by SANZEED » Tue Dec 18, 2012 2:10 pm

If you consider negative integers,then you must count negative factors.Then actually there will be 48 factors,not 24. :|
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