Problem:
How many positive factors of 36 are also multiples of 4?
Answer Choices:
A. 2
B. 3
C. 4
D. 5
E. 6
Solution:
The positive factors of 36 are 1,2,3,4,6,9,12,18, and 36. Of these, 4,12, and 36 are also multiples of 4.
OR
List the multiples of 4 through 36, then mark those which are factors of 36:
4,8,12,16,20,24,28,32,36.
OR
Since 36=2232, its positive factors are:
​2030,2130,22302031,2131,22312032,2132,2232​
Of these, only three are also multiples of 4=22.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions