✖️ 整数各位数字相乘Multiply Integer Digits

使用说明与常见问题How-to & FAQ

「整数各位数字相乘」是什么？What is the Multiply Integer Digits tool?

把每个整数的各位数字相乘（忽略符号与前导零处理按数字本身），可反复乘到只剩一位（数字根相关）。本地处理。Multiply the digits of each integer together (sign ignored for the product of digits). Optionally repeat until a single digit remains. Processed locally.

如何使用「整数各位数字相乘」？How do I use the Multiply Integer Digits tool?

在「整数各位数字相乘」中，把内容粘贴或输入到上方输入框，结果会实时显示在下方，点击「复制结果」即可复制。例如输入「25」，得到「10」。Paste integers, one per line or separated by spaces. Each result is the product of that number's digits (25 gives 10, and the sign is ignored); tick "Repeat to one digit" to keep multiplying until a single digit is left, and click "Copy result" to copy it.

怎样输入多个整数？How do I enter several integers?

每行一个，或用空格、逗号、分号分隔；可带千位逗号和下划线，负数前面加 -。One per line, or separated by spaces, commas or semicolons; thousands commas and underscores are fine, put - in front of negatives.

结果精确吗？Are the results exact?

精确。所有整数都按大整数（BigInt）处理，不经过浮点，超过 2^53 的数（例如 9007199254740993）也不会被舍入；几千上万行也是线性处理。Yes. Every value is handled as a big integer (BigInt) with no floating-point step, so numbers above 2^53 such as 9007199254740993 are never rounded; thousands of lines are processed in linear time.

和数字根有什么关系？How does this relate to the digital root?

反复将各位相乘会很快到一位数，但与各位相加得到的数字根不同（乘积遇 0 会变成 0）。Repeatedly multiplying digits reaches a single digit quickly, but it is not the digital root from summing digits (a 0 digit forces the product to 0).

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

例如在「整数各位数字相乘」中输入 25，输出为：10（⏎ 表示换行）。For example, the Multiply Integer Digits turns the input 25 into: 10 (⏎ marks a line break).

有哪些选项可以调整？What options can I adjust?

「整数各位数字相乘」的设置：可勾选：「乘到只剩一位」、「千位逗号」。改动任一选项后结果会按新设置重新生成。Settings in the Multiply Integer Digits — tick boxes: "Repeat to one digit", "Thousands commas". Changing any option regenerates the result with the new setting.

「整数各位数字相乘」免费吗？需要注册吗？Is the Multiply Integer Digits free? Do I need an account?

「整数各位数字相乘」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 Multiply Integer Digits is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.