➗ 找出全部因数Find All Divisors
列出一个整数的全部正因数(含 1 和它本身),可按行或逗号输出,并显示因数个数与之和。本地处理。List every positive divisor of an integer (including 1 and itself), as lines or commas, with the count and sum. Processed locally.
使用说明与常见问题How-to & FAQ
「找出全部因数」是什么?What is the Find All Divisors tool?
列出一个整数的全部正因数(含 1 和它本身),可按行或逗号输出,并显示因数个数与之和。本地处理。List every positive divisor of an integer (including 1 and itself), as lines or commas, with the count and sum. Processed locally.
如何使用「找出全部因数」?How do I use the Find All Divisors tool?
在「找出全部因数」中,把内容粘贴或输入到上方输入框,按需设置「分隔」,结果会实时显示在下方,点击「复制结果」即可复制。例如输入「12」,得到「1 ⏎ 2 ⏎ 3 ⏎ 4 ⏎ 6 ⏎ 12」。In the Find All Divisors: Paste or type into the input box, adjust "Separator"; the result appears below instantly — click "Copy result" to copy it. Example: "12" → "1 ⏎ 2 ⏎ 3 ⏎ 4 ⏎ 6 ⏎ 12".
含不含负数因数?Are negative divisors listed?
只接受正整数,只列出正因数。输入负数(例如 -12)会提示改输入它的绝对值;需要成对的 ± 因数时请自行加上负号。+12 与 12 相同。Only positive integers are accepted and only positive divisors are listed. A negative input such as -12 gives a message asking for its absolute value; add a minus yourself if you need ± pairs. +12 is the same as 12.
能算多大的数?How large can the number be?
最多 40 位。整数按大整数(BigInt)精确处理,先分解质因数(试除 + Miller–Rabin + Pollard rho),再由质因数组合出全部因数,所以 600851475143(= 71 × 839 × 1471 × 6857,16 个因数,和 610544148480)这类数也能立即算出。结果下方会写出因数个数、因数和与质因数分解。极少数难分解的大数会在时限内停下并明确提示,不会给出不完整的列表;因数超过 200000 个时也会提示。Up to 40 digits. Integers are handled exactly as big integers (BigInt): the number is factored first (trial division, Miller–Rabin and Pollard rho) and every divisor is built from the prime factors, so numbers such as 600851475143 (= 71 × 839 × 1471 × 6857, 16 divisors, sum 610544148480) are instant. The count, the sum and the prime factorisation are shown below the result. A rare hard-to-factor number stops at the time limit with a clear message instead of an incomplete list, and more than 200,000 divisors also gives a message.
输入和输出是什么样的?What does the input and output look like?
例如在「找出全部因数」中输入 12,输出为:1 ⏎ 2 ⏎ 3 ⏎ 4 ⏎ 6 ⏎ 12(⏎ 表示换行)。For example, the Find All Divisors turns the input 12 into: 1 ⏎ 2 ⏎ 3 ⏎ 4 ⏎ 6 ⏎ 12 (⏎ marks a line break).
有哪些选项可以调整?What options can I adjust?
「找出全部因数」的设置:「分隔」可选 每行一个、逗号、空格(默认 每行一个)。每次生成结果都按当前设置处理。Settings in the Find All Divisors — "Separator": One per line, Commas, Spaces (default One per line). The result always uses the current settings.
「找出全部因数」免费吗?需要注册吗?Is the Find All Divisors free? Do I need an account?
「找出全部因数」完全免费,无需注册或安装,打开网页即可使用,手机和电脑都能用;输入的内容只在你的浏览器本地处理。The Find All Divisors is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.