When we perform Gaussian elimination mod 2 on our exponent m

When we perform Gaussian elimination mod 2 on our exponent matrix, why is it advisable to eliminate entries in the columns that correspond to the largest primes in the factor base first?

Solution

Because the columns represent the exponents (mod p) of the primes in the factor base, where p is the prime.So, for example, if the factor base is {1, 2, 3, 13, 17, 19, 29} and Q(x) = 2317219, then the row belongs to this Q(x) should be (0, 1, 1, 0, 0, 1, 0).