There are four integer quotients obtained by dividing a four-digit number by its digits. The sum of these four quotients is still this four-digit number (for example, 4444 is one of them). How many four-digit numbers meet the requirements?
有一个四位数分别除以它的各位数字得到的四个整数商，这四个商的和还是这个四位数(例如4444就是其中的一个)求满足要求的四位数共有多少个？
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/2) + (1/4) + (1/8) + (1/8)</gadget>
<output>1</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">5 + 2 + (1/3) + (1/3) + (1/6) + (1/6)</gadget>
<output>8</output>

<result>8</result>