Problem on odd-even and factorization of a number

Question: Tell an odd number that is lesser than 50 and it has at least 5 factors.

Ans:

We have to first define what we call factors here:
Way 1: Non-trivial factors alone. That means we would exclude 1 and the number itself.

Way 2:
The number 1 and the number itself are the 'Trivial Factors' of a number.
We include both trivial and non-trivial factors.

If we look at Way 2, then 45 is an answer.
45 has factors: 1, 3, 5, 9, 15, 45

If we consider only non-trivial factors, then there is no number that is lesser than 50 and would yield five factors.

Let us approach the problem from back-to-forth. 

Since, the number should be odd, there would be no 2 in its factors.
So the lowest factor for any number could 3.

Now: Let us multiply 3 with 3: 3 * 3 = 9
Now we multiply 9 with 3: 27
Now we multiply 27 with 3: 81.
And 81 (that is 3 * 3 * 3 * 3) is greater than 50.

So, with Way 1: There is no answer to this question.

Tags: Mathematical Foundations for Data Science,