累进可除数（英語：Polydivisible number）是有以下特質的整數：首個位非零，而且由它首 n {\displaystyle n} 個位組成的數是 n {\displaystyle n} 的倍數。
例如345654:
而123456就非累进可除数，因為1234不是4的倍數。
累进可除数可以在不同的进位制中定義。本條目僅談論十進制中的情況。
累进可除数是趣味數學上的一道名題的一般化：
雖然9位的累进可除数有2492個，但唯一一個包含1至9的數字而不重覆的只有一個，是381,654,729。
若 k {\displaystyle k} 是 n − − --> 1 {\displaystyle n-1} 位的累进可除数，若有 10 k {\displaystyle 10k} 和 10 k + 9 {\displaystyle 10k+9} 之間有數可以被 k {\displaystyle k} 整除， k {\displaystyle k} 便可以擴充一個位，成為n位的累进可除数。若 n ≤ ≤ --> 10 {\displaystyle n\leq 10} ，必定可以由 n − − --> 1 {\displaystyle n-1} 位的累进可除数擴充成n位的累进可除数，且有多於一個可行的擴充辦法。反之，若 n > 10 {\displaystyle n>10} ， n {\displaystyle n} 越大，能夠擴充成為另一個累进可除数的辦法隨之而越少。因此，將累进可除数的分布畫成曲線圖，會得出一條鐘形曲線。
平均來說，每個 n − − --> 1 {\displaystyle n-1} 位的累进可除数擴充成n位的累进可除数有 10 n {\displaystyle {\frac {10}{n}}} 種方法。這產生了以下這條用以估計n位的累进可除数數目的公式（以 F ( n ) {\displaystyle F(n)} 表示 n {\displaystyle n} 位累进可除数的數目）：
將所有 n {\displaystyle n} 之值加起來套入此式，就得出所有累进可除数的數目：
最長的累进可除数有25位，等於360,852,885,036,840,078,603,672,5。
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