N is a square
N is a cube
N is an odd number
N is divisible by twelve prime numbers.
Find N
If N is both a square and a cube, it must be a 6th power.
smallest N = 3^6 * 5^6 * ... * 41^6
but the 12 primes can be much larger. Thee are tables of primes online for you to choose from.
To find the number N that satisfies the given conditions, we can approach it step by step:
1. N is a square: This means that N is a perfect square of an integer. We can start by listing the first few perfect squares until we find one that satisfies the other conditions.
2. N is a cube: Once we have a list of potential perfect squares, we can check if any of them are also perfect cubes. A perfect cube is a number that can be expressed as the cube of an integer.
3. N is an odd number: After identifying the numbers that are both perfect squares and perfect cubes, we can check if any of them are odd. An odd number is any number that is not divisible by 2.
4. N is divisible by twelve prime numbers: Finally, we need to check if any of the remaining numbers satisfy the condition of being divisible by exactly twelve prime numbers. A prime number is a number greater than 1 that is divisible only by 1 and itself.
By following these steps, we can find the value of N that satisfies all the given conditions.