Find the smallest number N such that:
The number of divisors of N is A.
The number of divisors of A is B.
The number of divisors of B is C.
The number of divisors of C is 3.
Details and assumptions
The divisors include 1 and the number itself. For example, the number of divisors of 10 is 4.
I have one feasible solution, not sure if it is optimal. You can find others for a check along the same lines.
C=4, 3 factors: 1,2,4
B=6, 4 factors: 1,2,3,6
A=12,6 factors: 1,2,3,4,6,12
N=72,12 factors: 1,2,3,4,6,8,9,12,18,24,36,72
its wrong
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To find the smallest number, N, that satisfies these conditions, we can follow a step-by-step approach:
1. Start with N = 1 and initialize a variable, count, to keep track of the number of divisors.
2. Check the number of divisors of N using a loop. Iterate from i = 1 to i <= N and check if N is divisible by i. If it is, increment the count by 1.
3. Check if the count is equal to A. If it is not, increment N by 1 and repeat steps 2 and 3 until the count is equal to A.
4. Once the count is equal to A, store the value of N in a new variable, X, to use it in the next step.
5. Repeat steps 2 to 4 for the number of divisors of A until the count is equal to B, using the stored value X.
6. Repeat steps 2 to 4 for the number of divisors of B until the count is equal to C, using the stored value X.
7. Repeat steps 2 to 4 for the number of divisors of C until the count is equal to 3, using the stored value X.
8. Once the count is equal to 3, the value of N is the smallest number that satisfies all the conditions.