Let $Z$ be a 6-digit positive integer, such as $247247$ , whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$ ?
A. 11
B. 19
C. 101
D. 111
E. 1111

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Worked solution

1. 2017 AMC 8 官方解析

翻译： $Z$ 是一个六位正整数，它的前三位和后三位完全一样．下面选项中的数一定是 $Z$ 的因数的是（　　）．
$Z = \overline{abcabc}$ 分解 $Z$ ， $Z = \overline{abc} \times 1001 = \overline{abc} \times 7 \times 11 \times 13$ ，所以选A．

Answer

A. 11

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Let ZZZ be a 6-digit positive integer, such as 247247247247247247, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of ZZZ?A. 11B. 19C. 101D. 111E. 1111

Worked solution

More questions on this topic

Let $Z$ be a 6-digit positive integer, such as $247247$ , whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$ ?
A. 11
B. 19
C. 101
D. 111
E. 1111