The P.G. Wodehouse Method Of Refactoring (2008)
basildoncoder.com2 pointsby svat3 comments
| n | factorization | products of two numbers
|-----|----------------|------------------------------------
| 50 | 2 * 5^2 | 1x50, 2x25, 5x10
| 60 | 2^2 * 3 * 5 | 1x60, 2x30, 3x20, 4x15, 5x12, 6x10
| 70 | 2 * 5 * 7 | 1x70, 2x35, 5x14, 7x10
| 75 | 3 * 5^2 | 1x75, 3x25, 5x15
| 80 | 2^4 * 5 | 1x80, 2x40, 4x20, 5x16, 8x10
| 84 | 2^2 * 3 * 7 | 1x84, 2x42, 3x28, 4x21, 6x14, 7x12
| 90 | 2 * 3^2 * 5 | 1x90, 2x45, 3x30, 5x18, 6x15, 9x10
| 96 | 2^5 * 3 | 1x96, 2x48, 3x32, 4x24, 6x16, 8x12
| 98 | 2 * 7^2 | 1x98, 2x49, 7x14 × | 0 1 2 3 4 5 6 7 8 9
---+------------------------------
0 | 0 0 0 0 0 0 0 0 0 0
1 | 0 1 2 3 4 5 6 7 8 9
2 | 0 2 4 6 8 10 12 14 16 18
3 | 0 3 6 9 12 15 18 21 24 27
4 | 0 4 8 12 16 20 24 28 32 36
5 | 0 5 10 15 20 25 30 35 40 45
6 | 0 6 12 18 24 30 36 42 48 54
7 | 0 7 14 21 28 35 42 49 56 63
8 | 0 8 16 24 32 40 48 56 64 72
9 | 0 9 18 27 36 45 54 63 72 81
That is, in decimal, only 37% of (up to) two-digit numbers can be written as products of two one-digit numbers. This fraction, which drops to 28% at n=100, only drops to 17% at n=2^64 (per the article). So it decreases VERY slowly, and it's nontrivial that it actually goes to 0.