How many positive whole numbers, including 1 , divide exactly into both 40 and 72 ?
(A) 9
(B) 12
(C) 4
(D) 2
(E) 5
Solution 1

The positive whole numbers that divide exactly into 40 are 1, 2, 4, 5, 8, 10, 20, 40 .

The positive whole numbers that divide exactly into 72 are $1,2,3,4,6,8,9,12,18,24,36,72$. The numbers that occur in both lists are 1, 2, 4, 8, or four numbers in total.

## Solution 2

The greatest common divisor of 40 and 72 is 8 .

Any common divisor of 40 and 72 is a divisor of the greatest common divisor (namely 8) and vice-versa.

Since the positive divisors of 8 are 1, 2, 4, and 8 , there are four such common positive divisors.

ANSWER: (C)