Smallest positive integer that includes among its factors perfect squares

1^2 = 1 ..... 2^2 = 4 ..... 3^2 = 9

4^2 = 16 ... 5^2 = 25 ... 6^2 = 36 ... 7^2 = 49 ... 8^2 = 64

10^2 = 100 ..... 11^2 = 121 ..... 12^2 = 144 ..... 13^2 = 169 ..... 14^2 = 196

15^2 = 225 ..... 16^2 = 256 ..... 17^2 = 289 ..... 18^2 = 324 ..... 19^2 = 361

20^2 = 400 ..... 21^2 = 441 ..... 22^2 = 484 ..... 23^2 = 529 ..... 24^2 = 576

25^2 = 625 ..... 26^2 = 676 ..... 27^2 = 729 ..... 28^2 = 784 ..... 29^2 = 841

30^2 = 900 ..... 31^2 = 961

The factors of 2304 are:

1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 256 288 384 576 768 1152 2304

The prime factors are: 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 or 2^8 * 3^2

2304 is the smallest positive integer that includes among its factors at least 10 perfect squares.