Product of digits

The only ways to separate 144 into 3 single digits are: 2,8,9/3,6,8/4,4,9/4,6,6

2,8,9 and 3,6,8 each have 3x2 combinations

4,4,9 and 4,6,6 each have 3 combinations

So the answer is 18

144 is a multiple of 3.

$\therefore$ One digit = 3 or 6 or 9

$\Rightarrow$ Product of other two digits = 48 or 24 or 16

$\Rightarrow$ Possible digits are = 368 or 944 or 982 or 664

368 and 982 can be arranged in 6 ways, 664 and 944 can be arranged in 3 ways

Total number of ways = 6+6+3+3 = 18

N = 100 A + 10 B + C

A = INT(N/ 100)

B = MOD(INT(N/ 10),10)

C = MOD(N,10)

(A)(B)(C) = 144

Count = 18

nice problem