数学题:乘积末尾有几个0
- 时间:2020-05-12 13:38:15
- 分类:数学世界
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数学题:乘积末尾有几个0?1*2*3*4……..*50得到的结果后有几个0?
数学题解答:积的末尾有一个0,可以理解为有一个因数10。有两个0,可以理解为有两个因数10,……依次类推。而10可以分解为:10=2*5,也就是说一个因数2和一个因数5便可以使积的末尾有一个0。
从1到50各数中,含有因数2的远远超过含有因数5的。所以只需算出这些数中,一个含有几个因数5,就可以确定积的末尾有几个0了。
从一到50中,5的倍数有5,10,15,……,50。分别是5的1倍到10倍,其中25和50都含有两个因数5,其余的只含有一个因数5。所以,这些数中一共含有:10+1+1=12(个)因数5,所以积的末尾有12个0。
经计算机验证,答案是正确的,如下图:
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