How do you factor, 45c + 10d?

We can't factor out a c or d, since we don't know c in terms of d, or vise versa. We thus can only factor out an integer. We see that both numbers are divisible by 5, so we factor out a 5, for a result of 5 (9c+2d). 9 and 2 do not have any common factors other than 1, so we have factored fully. Thus, the answer is 5 (9c+2d).