The greatest common factor (GCF) of 14 and 21 is 7.
So we can write 14 and 21 as the product of 7 and their corresponding quotients:
14 = 7 * 2
21 = 7 * 3
Now we can apply the distributive property and combine them:
14 + 21 = 7 * 2 + 7 * 3 = 7 * (2 + 3) = 7 * 5 = 35
The final answer is 35.