➗ 计算因数个数Calculate Number of Divisors

使用说明与常见问题How-to & FAQ

「计算因数个数」是什么？What is the Calculate Number of Divisors tool?

计算正整数的正因数个数 d(n)，可同时列出因数。本地处理。可设置「分隔」、「列出因数」。Count the positive divisors d(n) of a positive integer; optionally list them. Processed locally. Settings: Separator, List divisors.

如何使用「计算因数个数」？How do I use the Calculate Number of Divisors tool?

在「计算因数个数」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「6」。In the Calculate Number of Divisors: Paste or type into the input box, adjust "Separator"; the result appears below instantly — click "Copy result" to copy it. Example: "12" → "6".

含 1 和本身吗？Include 1 and n?

是，d(n) 统计全部正因数，包括 1 和 n 本身。例如 12 的因数是 1、2、3、4、6、12，d(12) = 6。Yes. d(n) counts every positive divisor, including 1 and n itself. For example, 12 has divisors 1, 2, 3, 4, 6, 12, so d(12) = 6.

多大的数可以算？How large a number can it handle?

最多 40 位。数字按大整数（BigInt）读入，用 Miller–Rabin 和 Pollard rho 分解质因数，再由 d(n) = (e₁+1)(e₂+1)… 求个数，结果下方会显示分解式；不经过浮点，所以 9007199254740993 这类超过 2^53 的数也精确。列出因数时最多列 100000 个。少数难分解的大数（例如两个约 20 位质数的乘积）可能在时限内分解不完，这时会提示“在时限内未能完全分解”，不会给出不完整的结果。Up to 40 digits. The number is read as a big integer (BigInt), factored with Miller–Rabin and Pollard rho, and the count comes from d(n) = (e₁+1)(e₂+1)…; the factorisation is shown below the result. There is no floating point, so numbers above 2^53 such as 9007199254740993 are exact. Listing shows up to 100,000 divisors. A few hard numbers (for example the product of two primes of about 20 digits each) may not factor within the time limit; you then get a "could not fully factor" message rather than an incomplete result.

输入和输出是什么样的？What does the input and output look like?

例如在「计算因数个数」中输入 12，输出为：6。For example, the Calculate Number of Divisors turns the input 12 into: 6.

有哪些选项可以调整？What options can I adjust?

「计算因数个数」的设置：「分隔」可选 每行一个、逗号（默认 每行一个）；可勾选：「列出因数」。每次生成结果都按当前设置处理。Settings in the Calculate Number of Divisors — "Separator": One per line, Commas (default One per line); tick boxes: "List divisors". The result always uses the current settings.

「计算因数个数」免费吗？需要注册吗？Is the Calculate Number of Divisors free? Do I need an account?

「计算因数个数」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 Calculate Number of 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.