Riuscita, I had problems really understanding the

concept to this one when I first saw it in the

Kaplan book. But the concept is easier to comprehend if you look at it backwards.

In order for a number to be the

greatest common divisor for two different positive integers that are

less than 144, we need to be able to multiply that number with two different positive integers and still get a result that is less than 144.

143 * 1 = 143; 143 * 2 = .... obviously this would be greater than 144. No need to calculate.

142 * 1 = 142; 142 * 2 = .... same as above

72 * 1 = 72; 72 * 2 = 144 .... 144 is not

less than 144.

71 * 1 = 71; 71 * 2 = 142 .... eureka! there we have it...

So the answer is 71.