2,520

A few days ago I read the factlet that 2,520 is the smallest number which is divisible by every number from 1 to 10. After a bit of playing with my calculator, I found that this is equal to 9 x 8 x 7 x 5. Why not 10, 6, 4, 3 and 2? Well, if a number is divisible by 40 (8 x 5), then it is also divisible by 10; if is is divisible by 9, then it is also divisible by 3; and if it is divisible by 8, then it is also divisible by 4 and 2. 6 is less immediately obvious, but 2,520 is divisible by 72 (9 x 8), so it is also divisible by 6 (and 12). Another way of reaching the same conclusion is to break 9, 8, 7 and 5 into their smallest divisors (3 x 3) x (2 x 4) x 7 x 5, which equals 3 x (3 x 2) x 4 x 5 x 7, which is clearly divisible by 6. That, in fact, which I didn’t notice at first but the Wikipedia page about the number has just informed me, makes it equal to 3 x 4 x 5 x 6 x 7.

2520 is the postcode for Wollongong, but I don’t think there’s anything mathematically significant about that.

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2 thoughts on “2,520

  1. Pingback: Trains of thought | Never Pure and Rarely Simple

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