The remainder when the product 1492· 1776· 1812· 1996 is divided by 5 is

AMC 8 1996 Problem 15

AMC8 1996 年第 15 题

余数与同余★★★☆☆

The remainder when the product

1492\cdot 1776\cdot 1812\cdot 1996

is divided by 5 is

乘积

1492\cdot 1776\cdot 1812\cdot 1996

除以 5 的余数是

正确答案 · Correct Answer

解析 · Solution

Solution 1

To determine a remainder when a number is divided by 5, you only need to look at the last digit. If the last digit is 0 or 5, the remainder is 0. If the last digit is 1 or 6, the remainder is 1, and so on.

To determine the last digit of

1492\cdot 1776\cdot 1812\cdot 1996

, you only need to look at the last digit of each number in the product. Thus, we compute

2\cdot 6\cdot 2\cdot 6 = 12^2 = 144

. The last digit of the number

1492\cdot 1776\cdot 1812\cdot 1996

is also 4, and thus the remainder when the number is divided by 5 is also 4, which gives an answer of

E

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