85问答库 > 在1×2×3×4×5乘等等等乘2013的末尾连续有多少个0？

在1×2×3×4×5乘等等等乘2013的末尾连续有多少个0？

2025-04-02 20:37:27
推荐回答（1个）
回答1：

连续数之积位数零的个数与其中质因数2与5的个数有关
2的个数比5多
所以只计算5的个数即可
1到2013中是5的倍数有2013÷5=402……3，402个
是5²=25的倍数有2013÷25=80……13
是5³=125的倍数有2013÷125=16……13
是5^4=625的倍数有2013÷625=3……138
所以含质因数5的个数是402+80+16+3=501
即连乘的积末尾有501个0

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