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

Question

• 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?

Answer 1

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

Answer 2

to be odd, it cannot have 2 as a factor.

Answer 3

Of course, good checkup oobleck.

Answer 4

are you sure, you answerd all the points of it.

Answer 5

Please anser my question. Urgent!

If any one can solve; please do and share the answer in step by step.

Answer 6

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

Answer 7

Hey 👋

Answer 8

Please answer the question in detail.

In step by step.

Answer full, not hints.

Please Answer ASAP.

Answer 9

I understand your approach; thanks

Answer 10

Please answer the question in detail.

In step by step.

Answer full, not hints.

Please Answer ASAP

Answer 11

12/3/2008
Birth of date