找一组数字的最大公因数很容易，但要先掌握方法。找两个数字的最大公因数，要先把两个数字的因数列出来，然后按照下文步骤进行。
步骤
方法 1 的 2:
比较公因数
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/6\/6b\/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
1
列出几个数字的因数。找最大公因数不一定非要用分解质因数法，你可以分别列出这组数字的因数。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/0\/0d\/Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/0\/0d\/Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
2
比较几组数字，找出最大公因数。
方法 2 的 2:
质因数分解法
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/a\/a5\/Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/a\/a5\/Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
1
把每个数字分解成几个质数相乘的形式。质数指的是除了1和此整数自身外，无法被其他自然数整除的数。举几个例子，5，17，97，331都是质数。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/90\/Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/90\/Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
2
找出共有的质数。找出这组数字共有的质数，可能是好几个。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/9\/94\/Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/9\/94\/Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
3
计算。如果只有一个共同的质数，那这个数字就是它们的最大公因数。如果有好几个共同的质数，就把它们相乘，得出的数就是最大公因数。
-
{"smallUrl":"https:\/\/www.zenmeban.com\/images_en\/thumb\/8\/8a\/Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg\/v4-460px-Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg","bigUrl":"https:\/\/www.zenmeban.com\/images\/thumb\/8\/8a\/Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg\/v4-728px-Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><\/div>"}
4
研究这个例子。研究一下给出的例子来巩固质因数分解法。
小提示
- 质数指的是除了1和此整数自身外，无法被其他自然数整除的数。
- 你知道吗，欧几里得早在公元前三世纪就创造出了计算两个自然数或多项式最大公因数的算法。