what is the highest common factor of 16 and 44?

2                                         

Try dividing each number into its Prime factors, e.g. :18 /2=9/3=3/3=1. So, the Prime factors of 18 are: 2 X 3 X 3. Do this for both numbers and see, by inspection, which Prime factor is the largest that divides both of them evenly. Hint: your answer should be an EVEN number. Good luck.

2 

16 = 2 x 2 x 2 x 2

11 = 2 x 2  x 11

Take the common factors  from both lists   2 x 2  = 4

The highest common factor is 4