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?
Hey 👋
to be odd, it cannot have 2 as a factor.
Please answer the question in detail.
In step by step.
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I understand your approach; thanks
12/3/2008
Birth of date
Of course, good checkup oobleck.
are you sure, you answerd all the points of it.
Please anser my question. Urgent!
If any one can solve; please do and share the answer in step by step.
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
Please answer the question in detail.
In step by step.
Answer full, not hints.
Please Answer ASAP
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