However, simply squaring many random numbers mod "n" produces a very large number of different prime factors, and so very long vectors and a very large matrix. The trick is to look specifically for numbers "a" such that "a"2 mod "n" has only small prime factors (they are smooth numbers). They are harder to find, but using only smooth numbers keeps the vectors and matrices smaller and more tractable. The quadratic sieve searches for smooth numbers using a technique called sieving, discussed later, from which the algorithm takes its name.