It is known that the greatest common divisor of a and b is 14, and the least common multiple of a and c, b and c is 350. And a≤b. So how many groups of natural numbers a, b, and c satisfy the conditions?
已知a与b的最大公约数是14，a与c、b与c的最小公倍数都是350．且a≤b．那么满足条件的自然数a、b、c共有多少组？
<gadget id="calculator">5 * 4</gadget>
<output>20</output>

<result>20</result>