Put the natural numbers 4, 8, 12, ... 2004, 2008, 2012 in a circle clockwise, each number has a greatest common divisor with the number adjacent to it clockwise, then the sum of all these greatest common divisors is How many.
把自然数4，8，12，…2004，2008，2012按顺时针围成一圈，每个数都与它顺时针相邻的那个数有一个最大公约数，则所有这些最大公约数之和是多少．
<gadget id="calculator">2_012 - 4</gadget>
<output>2_008</output>

<gadget id="calculator">2_008 / 4</gadget>
<output>502</output>

<gadget id="calculator">1 - 1</gadget>
<output>0</output>

<gadget id="calculator">502 + 0</gadget>
<output>502</output>

<gadget id="calculator">4 * 502</gadget>
<output>2_008</output>

<result>2_008</result>