this post was submitted on 19 Dec 2023
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did you know 1209 is a prime number? or maybe not, I'm just a cat :3
TIL cats are really bad at math.
credit: usedsoil on instagram
1209 is 3 times 13 times 31, and cats are better at typing than they are at math.
In base 10, the sum of the digits of any number that is divisible by 3 is also divisible by 3, so 1+2+0+9=12, implies 1209 is divisible by 3.
Likewise, 1001 is divisible by 13, so if you split a number in base 10 every 3 digits, and subtract/add alternating sets of numbers, if the result is divisible by 13, the original number is, too. 209-1 is 208, which is obviously divisible by 13, so 1209 is, too.
Divisibility by 31 in base 10 is harder to check, but 999998 is divisible by 31, as is 999999999999999, so you can just split the number every 15 digits, and add those together, and if the sum is divisible by 31... I'm talking about math to a cat.
did you know that adding up all the divisors of 1209 and swapping the last two digits gives you a number that can be represented as the sum of two cubes in two different ways? or maybe not, I'm just a cat :3