Each of the integers 334 and 419 has digits whose product is 36 . How many 3-digit positive integers have digits whose product is 36 ?
(A) 21
(B) 15
(C) 18
(D) 24
(E) 12
The single-digit divisors of 36 are: $1,2,3,4,6$, and 9 .

The groups of 3 of these digits whose product is 36 are: $1,4,9 ; 1,6,6 ; 2,2,9 ; 2,3,6$, and $3,3,4$.

Next, we count the number of ways to arrange each of these 5 groups of digits.

The digits 1, 4, 9 can be arranged to form: 149,194,419,491,914, 941 .

The digits 1,6,6 can be arranged to form: 166,616,661.

The digits 2, 2, 9 can be arranged to form: 229, 292, 922 .

The digits 2, 3, 6 can be arranged to form: $236,263,326,362,623,632$.

The digits $3,3,4$ can be arranged to form: $334,343,433$.

The number of 3-digit positive integers having digits whose product is 36 is $6+3+3+6+3=21$.