How many different positive integers divisible by 4 can be formed using at least one of the digits 1, 2, 3, 4, and 6 exactly once and no other digits? For example, 12 counts, but 512 does not.
(4, 12, 16, 24, 32, 36, 64, 124, 132, 136, 164, 216, 236, 264, 312, 316, 324, 364, 412, 416, 432, 436, 612, 624, 632, 1236, 1264, 1324, 1364, 1432, 1436, 1624, 1632, 2136, 2164, 2316, 2364, 2416, 2436, 3124, 3164, 3216, 3264, 3412, 3416, 3612, 3624, 4132, 4136, 4216, 4236, 4312, 4316, 4612, 4632, 6124, 6132, 6312, 6324, 6412, 6432, 12364, 12436, 13264, 13624, 14236, 14632, 16324, 16432, 21364, 21436, 23164, 23416, 24136, 24316, 31264, 31624, 32164, 32416, 34216, 34612, 36124, 36412, 41236, 41632, 42136, 42316, 43216, 43612, 46132, 46312, 61324, 61432, 63124, 63412, 64132, 64312) >>Total = 97 integers divisible by 4