# 247: Factoring the Time

Factoring the Time |

Title text: I occasionally do this with mile markers on the highway. |

## Explanation

Cueball is bored, so he has been calculating the prime factors of the time shown on the clock. The prime factor of a positive number is a number which could be divided only by prime numbers. Cuball is 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 exactly one minute to determine this, which is nearly impossible to be done by a human brain..

In the title text, Randall claims he applies the same challenge to highway location 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.

## Transcript

- [One man is sitting at a computer. Cueball sits at a separate desk. There is a clock which reads 2:53.]
- Cueball: 253 is 11x23
- Man at computer: What?
- Cueball: I'm factoring the time.
- Cueball: I have nothing to do, so I'm trying to calculate the prime factors of the time each minute before it changes.
- Cueball: It was easy when I started at 1:00, but with each hour the number gets bigger
- Cueball: I wonder how long I can keep up.
- [Man at desk reaches back and touches the clock.]
*BEEP*- [Clock now reads 14:53.]
- Cueball: Hey!
- Man at computer: Think fast.

## Trivia

- There is a widget for OS X to display the current time and its prime factors.

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