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a [[number]].
- Significantly harder to factor than [[405]], which I find interesting.
- I think the fact that 405 and 406 are adjacent in the number line and have wildly differing difficulties of factorization probably says something about the nature of numbers? analyzing this fact can probably lead to interesting relations
- [[203]] * 2 but then I’m stumped, 203 could be a prime. I hope it is, maybe?
- It’s clearly not divisible by 3 if you already checked [[406]] (sum of digits 10, not divisible by 3), but I still checked out of custom. While doing this, remembering which numbers you don’t have to check is useful as it prevents duplicate work. Still I’m not concerned about repeating checks because I enjoy them.
- There is a bound for possible divisors we have to check; the bound is the square root of 203. That means that we may have gained some equity by not having taken the square root of 406, potentially harder to calculate than that of 203.
- In this case, though, the square root of 400 comes easier (to me): 20.
- But because we need to check divisors, we’ll want the tighter bound. 203 can’t be divisible by 5, can it be divisible by 7?
- 7 * 17 is 119, I know because they are my favourite numbers — is this useful? It tells me that in 203 ?= 7 * [[x]], X is bound to be lower than 34.
- Then it occurs to me 210, which is near 203, is clearly 7 * 30 because 21 is 7 * 3.
- And lo and behold, 210-203 is 7 :) So we got our answer:
- [[203]] is [[7]] * 29]]
- [[406]] is [[2]] * [[7]] * [[29]]
- Beautiful!