AMC8 1996

AMC8 1996 · Q15

AMC8 1996 · Q15. It mainly tests Remainders & modular arithmetic, Digit properties (sum of digits, divisibility tests).

The remainder when the product $1492 \cdot 1776 \cdot 1812 \cdot 1996$ is divided by 5 is

$1492 \cdot 1776 \cdot 1812 \cdot 1996$ 的乘积除以 5 的余数是

(A) 0 0

(B) 1 1

(D) 3 3

(E) 4 4

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): The last digit of a product is determined by the product of the last digits of the factors. Since $2\cdot 6\cdot 2\cdot 6=144$, the last digit of the product is $4$. Since multiples of $5$ end in $0$ or $5$, any number with last digit $4$ leaves a remainder of $4$ when divided by $5$.

答案（E）：一个乘积的末位数字由各个因数末位数字的乘积决定。因为 $2\cdot 6\cdot 2\cdot 6=144$，所以该乘积的末位数字是 $4$。由于 $5$ 的倍数的末位是 $0$ 或 $5$，任何末位为 $4$ 的数除以 $5$ 都会余 $4$。

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