63³-343 = 261801
Factor the following integer:
261'801
The sum of the digits of 261801 is 2 + 6 + 1 + 8 + 0 + 1 = 18, which is divisible by 9. This means 261801 is too.
261801 = 9×29089:
261801 = 9×29089
9 = 3^2:
261801 = 3^2×29089
Because 29089 is odd, only test odd numbers for divisibility.
29089 is not divisible by 3, 5, 7, 9, 11, 13, 15 or 17.
29089 = 19×1531 which means 29089 is divisible by 19:
261801 = 3^2×19×1531
3 is prime:
261801 = 3^2×19×1531
Because 19 is odd, only test odd numbers for divisibility.
19 is not divisible by 3.
Since 19 is not divisible by any integer up to 4, it is prime:
261801 = 3^2×19×1531
Because 1531 is odd, only test odd numbers for divisibility.
1531 is not divisible by 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37 or 39.
Since 1531 is not divisible by any integer up to 39, it is prime:
261801 = 3^2×19×1531
There are 2 copies of 3, 1 copy of 19 and 1 copy of 1531 in the product:
Answer: 261801 = 3^2×19×1531
as a whole number.
which is where you started from.