What is the greatest possible common divisor of two different positive integers which are less than 144?
Can someone explain why the answer is 71 if we assume that the integers are 143 and 142? Pick:
A) 143	B) 142	C) 72	D) 71	E) 12
First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.   Think:   2 and 3 have GCD (greatest common divisor) of 1   2 and 4 have GCD of 2.   3 and 4 have GCD (greatest common divisor) of 1   So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.   Now think: 143 = 11 * 13   The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.   142 = 2*71   The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)   Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.
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What is the greatest possible common divisor of two different positive integers which are less than 144?
Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?