The first step is to express both numbers in terms of their prime factors.
the prime factors of 14 are 2 * 7
the prime factors of 42 are 2 * 3 * 7
Now, we would pick the factors that occur most. We can see that 2 is common to both numbers but it appears only once. 7 is also common to both numbers. The other prime factor, 3 is not common to both numbers.
Thus, the greatest common factor is 2 * 7 = 14