5040 and other Anti-Prime Numbers - Numberphile
Audible: http://www.audible.com/numberphile (free trial) Dr James Grime discusses highly composite numbers. More links & stuff in full description below ↓↓↓ Continues and extra footage:...
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Sometimes it's useful to have a number which has lots of factors. Like the number 12 which can be divided by 2 and 3 and 4 and 6 and 12 itself. We find these things useful sometimes. The ancient Greek philosopher Plato He thought the best choice for something like this was the number 5040. He thought this was the best choice because it had loads of divisors, lots of factors. So, 1 divides into it obviously. 2 divides, 3, 4, 5, 6, 7 divides, 8 divides, 9 divides, 10 divides So all the numbers up to 10 divide, 12 divides into it as well, And it's got 60 divisors all together. So Plato was thinking this is the best number you could have for, like say, a city. If the population of a city was 5040 you could divide that up into all kind of different ...
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Sometimes it's useful to have a number which has lots of factors. Like the number 12 which can be divided by 2 and 3 and 4 and 6 and 12 itself. We find these things useful sometimes. The ancient Greek philosopher Plato He thought the best choice for something like this was the number 5040. He thought this was the best choice because it had loads of divisors, lots of factors. So, 1 divides into it obviously. 2 divides, 3, 4, 5, 6, 7 divides, 8 divides, 9 divides, 10 divides So all the numbers up to 10 divide, 12 divides into it as well, And it's got 60 divisors all together. So Plato was thinking this is the best number you could have for, like say, a city. If the population of a city was 5040 you could divide that up into all kind of different ...
