## ক্ষুদ্রতম সংখ্যা

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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always 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.
nisha
Posts: 30
Joined: Tue Dec 07, 2010 8:00 pm

### ক্ষুদ্রতম সংখ্যা

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

jhal_muri
Posts: 6
Joined: Sun Sep 11, 2011 1:58 am

### Re: ক্ষুদ্রতম সংখ্যা

if u mean positive integer,then it is 24!

nafistiham
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### Re: ক্ষুদ্রতম সংখ্যা

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.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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as-if
Posts: 1
Joined: Tue Oct 25, 2011 5:51 pm

### Re: ক্ষুদ্রতম সংখ্যা

ans is 420

jhal_muri
Posts: 6
Joined: Sun Sep 11, 2011 1:58 am

### Re: ক্ষুদ্রতম সংখ্যা

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

sm.joty
Posts: 327
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Location: Dhaka

### Re: ক্ষুদ্রতম সংখ্যা

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
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Prosenjit Basak
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Joined: Wed Nov 28, 2012 12:48 pm

### Re: ক্ষুদ্রতম সংখ্যা

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. Give me advice if I am wrong
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SANZEED
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