本文尝试将数论中的一些基本理论推广到序数上。推广过程中，主要的困难是序数的加法和乘法没有交换律，且只有一个方向的分配律。 我们定义了素序数，并给出了一个无穷素序数的通项公式，然后给出了一个任意序数的唯一分解，或者说是唯一的因式分解。我们定义了最大公因数与最小公倍数，然后推广了数论中的定理(a,b)[a,b]=ab. 此外，我们还对辗转相除法做了一些研究。

In this paper, we try to generalize some arithmetic theorem in number theory to ordinals. The main difficulty is, addition and multiplication of infinite ordinals have no commutativity, and have only one side distributivity. We define the prime ordinal and give a general term of infinite ones, then give a unique decomposition, or in other words, a unique factorization , of all ordinals. We define the greatest common divisor and the least common multiple, generalize the theorem (a,b)[a,b]=ab . And we also have some conclusion about Euclidean Algorithm, including a necessary condition of a kind of equation have a solution.