Karen says that 6 is a common factor of 2 and 3 ken says that 6 is a common multiple of 2 and 3 who is correct

6 is a common multiple of 2 and 3...so Ken is correct

think of multiples like multiplication tables
2 * 1 = 2
2 * 2 = 4
2 * 3 = 6
so 2,4,and 6 are multiples of 2
same with 3..
3 * 1 = 3
3 * 2 = 6
3 * 3 = 9
so 3,6, and 9 are multiples of 3
so 6 is a common multiple of 2 and 3.

factors...they are what can be divided into a number...
6 has factors of 2 and 3because they both go into 6 evenly
but 6 is not a factor of 2 or 3 because 6 wont go into them evenly