Which of the following is the greatest

lheiannie07 wrote:Which of the following is the greatest possible common divisor of two different positive integers, both smaller than 124?

A. 123.
B. 122.
C. 63.
D. 62.
E. 61.

The key word here is different

If the two numbers were allowed to be the same, then we could use 123 and 123, in which case, the GCD = 123

However, since the two numbers must be DIFFERENT, then we might first try to do something with 123 and some other number.
Since 123 = (3)(41), we can see that, in order to MAXIMIZE the GCD of the two numbers, the other number must be 41
So, 123 and 41 have a GCD of 41

Now let's try 122 and some other number.
Since 122 = (2)(61), we can see that, in order to MAXIMIZE the GCD of the two numbers, the other number must be 61
So, 122 and 61 have a GCD of 61

Following this logic, we can see that 122 and 61 will MAXIMIZE the GCD of the 2 numbers.

So, the correct answer is E