Asked by sdvds

Find the smallest positive integer N that satisfies all of the following conditions:



• N is a square.



• N is a cube.



• N is an odd number.



• N is divisible by twelve prime numbers.



How many digits does this number N have?

Answers

Answered by mathhelper
The trouble is the divisibility by the first 12 prime numbers,
so it must be a multiple of 2*3*5*7*11*13*17*19*23*29*31*37

To be odd it must look like 2K+1

to be a square it must look like (2K+1)^2, and it must also be a cube
it must contain (2K+1)^6

so, it must have the form:
2*3*5*7*11*13*17*19*23*29*31*37(2K+1)^6
when K = 0, we get
2*3*5*7*11*13*17*19*23*29*31*37(1)^6
= 7.420738135... x 10^12
which would be 13 digits long
Answered by oobleck
to be odd, it cannot have 2 as a factor.
Answered by mathhelper
Of course, good checkup oobleck.
Answered by sdvds
are you sure, you answerd all the points of it.
Answered by sdvds
Please anser my question. Urgent!

If any one can solve; please do and share the answer in step by step.
Answered by mathhelper
obviously we have to take out the factor of 2 since multiplying anything
by 2 would make it even, so

3*5*7*11*13*17*19*23*29*31*37
Answered by It Girl
Hey 👋
Answered by sdvds
Please answer the question in detail.

In step by step.

Answer full, not hints.

Please Answer ASAP.
Answered by tony
I understand your approach; thanks
Answered by sdvds
Please answer the question in detail.

In step by step.

Answer full, not hints.

Please Answer ASAP
Answered by Komal battu
12/3/2008
Birth of date
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