8,549,176,320 is the unique 10-digit number that contains each digit 0–9 exactly once (a pandigital number) and is divisible by every integer from 1 through 10.
Key properties, succinctly:
Pandigital: uses each digit 0,1,2,3,4,5,6,7,8,9 exactly once.
Divisibility by 1–10: for every n in {1,2,…,10}, 8,549,176,320 ÷ n is an integer.
Divisible by 2, 4, 5, 8: ends with 0 (even), last two digits 20 (divisible by 4), last three 320 (divisible by 8), ends with 0 gives divisibility by 5 and 10.
Divisible by 3 and 9: sum of digits = 0+1+2+3+4+5+6+7+8+9 = 45, divisible by 3 and 9.
Divisible by 6: divisible by 2 and 3.
Divisible by 7: 8,549,176,320 ÷ 7 = 1,221,310,903 (integer).