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The Clock Game is a recreational mathematics game that you can play anytime anywhere. First, you take the time, for example right now it's 12:34, you drop the colon and treat it as a whole number 1234. Then, you reduce the number to its prime factors in a minuete.

1234=2x117

117=3x39, 1234=2x(3x39)

39=3x13, 117=3x(3x13), 1234=2x(3x(3x13))

And 13 has no factors except for 1 and itself.

So, the prime factors of 1234 are 2,3,3 and 13.


Prime Numbers

Such numbers found on a clock are prime numbers and therefore cannot be reduced into prime factors except 1 and itself.

1:01, 1:03, 1:07, 1:09, 1:13, 1:27, 1:31, 1:37, 1:39, 1:49, 1:51, 1:57, 2:11, 2:23, 2:27, 2:29, 2:33, 2:39, 2:41, 2:51, 2:57, 3:07, 3:11, 3:13, 3:17, 3:31, 3:37, 3:47, 3:49, 3:53, 3:59, 4:01, 4:09, 4:19, 4:21, 4:31, 4:33, 4:39, 4:43, 4:49, 4:57, 5:03, 5:09, 5:21, 5:23, 5:41, 5:47, 5:57, 6:01, 6:07, 6:13, 6:17, 6:19, 6:31, 6:41, 6:43, 6:47, 6:53, 6:59, 7:01, 7:09, 7:19, 7:27, 7:33, 7:39, 7:43, 7:51, 7:57, 8:09, 8:11, 8:21, 8:23, 8:27, 8:29, 8:39, 8:53, 8:57, 8:59, 9:07, 9:11, 9:19, 9:29, 9:37, 9:41, 9:47, 9:53, 10:09, 10:12, 10:19, 10:21, 10:31, 10:33, 10:39, 10:49, 10:51, 11:03, 11:09, 11:17, 11:23, 11:29, 11:51, 11:53, 12:01, 12:13, 12:17, 12:23, 12:29, 12:31, 12:37, 12:49, 12:59.

And on a 24-hour clock:

13:01, 13:03, 13:07, 13:19, 13:21, 13:27, 14:09, 14:23, 14:27, 14:29, 14:33, 14:39, 14:47, 14:51, 14:53, 14:59, 15:11, 15:23, 15:31, 15:43, 15:49, 15:53, 15:59, 16:01, 16:07, 16:09, 16:13, 16:19, 16:21, 16:27, 16:37, 16:57, 17:09, 17:21, 17:23, 17:33, 17:41, 17:47, 17:53, 17:59, 18:01, 18:11, 18:23, 18:31, 18:47, 19:01, 19:07, 19:13, 19:31, 19:33, 19:49, 19:51, 20:03, 20:11, 20:17, 20:27, 20:29, 20:39, 20:53, 21:11, 21:13, 21:29, 21:31, 21:37, 21:41, 21:43, 21:53, 22:03, 22:07, 22:13, 22:21, 22:37, 22:39, 22:43, 22:51, 23:09, 23:11, 23:33, 23:39, 23:41, 23:47, 23:51, 23:57, 0:02, 0:03, 0:05, 0:07, 0:11, 0:13, 0:17, 0:19, 0:23, 0:29, 0:31, 0:37, 0:41, 0:43, 0:47, 0:53, 0:59.

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