What is the greatest possible common divisor of two different positive integers which are less than 144?
A. 143
B. 142
C. 72
D. 71
E. 12
No two consecutive numbers share a common divisor greater than 1. For example, let's look at 5 and 6? It is 1.
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
If you were to select two numbers less than 5 with the greatest GCD, you should select 2 and 4, not 3 and 4.
143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71.
Can a 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.
D.
No comments:
Post a Comment