Explanation:
Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;
2, 3, 5, 7, 9, 15, 17, 19, 21, 23
Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.
Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.