The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 24?
1138 1146 1164 1183 1226 1234 1243 1262 1318 1324 1342 1381 1416 1423 1432 1461 1614 1622 1641 1813 1831 2126 2134 2143 2162 2216 2223 2232 2261 2314 2322 2341 2413 2431 2612 2621 3118 3124 3142 3181 3214 3222 3241 3412 3421 3811 4116 4123 4132 4161 4213 4231 4312 4321 4611 6114 6122 6141 6212 6221 6411 8113 8131 8311 Total = 64 such numbers
