More deep analyses for multiplication of large integers is given using the algorithm of divide and conquer.Based on the formerly algorithm of divide and conquer

we divide each of large integers into

k(2≤k≤n

) parts which are the same size.It is proven that we can reduce the times of multiplication from

k

2

to

k(k

+1)/2 in the product of two integers.The complexity for calculating the product of two large integers is given and is proven to be the lowest when we divide each of large integers into two parts which are the same size.Furthermore

it is shown to be reasonable to divide each of two large integers into two parts using the algorithm of divide and conquer.