247: Factoring the Time

Explain xkcd: It's 'cause you're dumb.
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Factoring the Time
I occasionally do this with mile markers on the highway.


Cueball is bored and so he has been calculating the prime factors of the time shown on the clock. He's been doing this for almost two hours (from 1:00 pm to 2:53 pm). The number 2 is the smallest prime but is not a factor of 253, which is an odd number. The smallest prime factor of 253 is 11, which makes the other factor 23.

His co-worker decides to mess with Cueball and so he switches the clock from 12-hour time (2:53 pm) to 24-hour time (14:53). This makes factorization more difficult, as the time now shown is a four digit number rather than a three digit number. The number 1,453 is actually a prime number and so has no factors but one and itself; Cueball has only one minute to determine this. Note that the time to determine the prime factors of a number is the greatest when the number is itself prime.

Finding prime factors is not a trivial matter; the difficulty of factoring large numbers is the fundamental protection behind Public-key cryptography (but it uses much larger numbers).

This comic may also be play on the phrase "factoring the time", which means taking time to make sure one has sufficient time.

The title text refers to a similar challenge involving mile markers. At highway speeds (60+ mph), they would show up at least once per minute. Combined with the need to also concentrate on driving, factorizing numbers in the allowed time becomes much more difficult.


Cueball: 253 is 11x23
Man at computer: What?
Cueball: I'm factoring the time.
Cueball: I wonder how long I can keep up.
[Man at desk reaches back and touches the clock.]
[Clock now reads 14:53.]
Cueball: Hey!
Man at computer: Think fast.




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