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
Basically you do long division by every prime less than 100.
I don’t understand, its factors are 101 and 109, both are more than 100.
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
That’s funny. “100” was a stand-in for sqrt(11009), I didn’t anticipate that all factors would actually be above 100.