Well, you check if it’s a multiple of every prime below sqrt(11009) ~= 105.
Though if you suspect he’s intentionally chosen a tricky number, a product of two large primes, you can look at the square numbers larger than 11009. In this case
11025 = 105^2, and
11025-11009 = 16 = 4^2, so
11009 = 105^2 − 4^2 = (105+4)(105-4) = 109×101
Well, you check if it’s a multiple of every prime below sqrt(11009) ~= 105.
Though if you suspect he’s intentionally chosen a tricky number, a product of two large primes, you can look at the square numbers larger than 11009. In this case 11025 = 105^2, and 11025-11009 = 16 = 4^2, so 11009 = 105^2 − 4^2 = (105+4)(105-4) = 109×101