가로의 길이가 24cm, 세로의 길이가 54cm, 높이가 60cm인 직육면체의 부피는 다음과 같이 계산할 수 있습니다.
부피 = 가로 × 세로 × 높이 = 24cm × 54cm × 60cm = 77760cm³
만들 수 있는 정육면체의 크기가 같아야 하므로, 정육면체의 부피는 77760cm³의 약수여야 합니다.
77760의 약수를 구해보면 다음과 같습니다.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 4096, 5120, 6144, 7680, 8192, 10240, 12288, 15360, 16384, 20480, 24576, 30720, 32768, 40960, 49152, 61440, 65536, 81920, 98304, 122880, 131072, 163840, 196608, 245760, 262144, 327680, 393216, 491520, 524288, 655360, 786432, 983040, 1048576, 1310720, 1572864, 1966080, 2097152, 2621440, 3145728, 3932160, 4194304, 5242880, 6291456, 7864320, 8388608, 10485760, 12582912, 15728640, 16777216, 20971520, 25165824, 31457280, 33554432, 41943040, 50331648, 62914560, 67108864, 83886080, 100663296, 125829120, 134217728, 167772160, 201326592, 251658240, 268435456, 335544320, 402653184, 503316480, 536870912, 671088640, 805306368, 1006632960, 1073741824, 1342177280, 1610612736, 2013265920, 2147483648, 2684354560, 3221225472, 4026531840, 4294967296, 5368709120, 6442450944, 8053063680, 8589934592, 10737418240, 12884901888, 16106127360, 17179869184, 21474836480, 25769803776, 32212254720, 34359738368, 42949672960, 51539607552, 64424509440, 68719476736, 85899345920, 103079215104, 128849018880, 137438953472, 171798691840, 206158430208, 257698037760, 274877906944, 343597383680, 412316860416, 515396075520, 549755813888, 687194767360, 824633720832, 1030792151040, 1099511627776, 1374389534720, 1649267441664, 2061584302080, 2199023255552, 2748779069440, 3298534883328, 4123168604160, 4398046511104, 5497558138880, 6597069766656, 8246337208320, 8796093022208, 10995116277760, 13194139533312, 16492674416640, 17592186044416, 21990232555520, 26388279066624, 32985348833280, 35184372088832, 43980465111040, 52776514533248, 65970697666560, 70368744177664, 87960930222080, 105553029066496, 131941395333120, 140737488355328, 175921860444160, 211106058132992, 263882790666240, 281474976710656, 351843720888320, 422212116265984, 527765145332480, 562949953421312, 703687441776640, 844424232919552, 1055530290664960, 1125899906842624, 1407374883553280, 1688849860269056, 2111060581329920, 2251799813685248, 2814749767106560, 3377699720538112, 4222121162659840, 4503599627370496, 5629499534213120, 6755399441056768, 8444242329195520, 9007199254740992, 11258999068426240, 13510798882111488, 16888498602690560, 18014398509481984, 22517998136852480, 27021597764222976, 33776997205381120, 36028797018963968, 45035996273704960, 54043195528445952, 67553994410567680, 72057594037927936, 90071992547409920, 108086391056891904, 135107988821114880, 144115188075855872, 180143985094819840, 216172782113783808, 270215977642229760, 288230376151711744, 360287970189639680, 432345564227567616, 540431955284459520, 576460752303423488, 720575940379279360, 864691128455135232, 1080863910568919040, 1152921504606846976, 1441151880758558720, 1729382256910270464, 2161727821137838080, 2305843009213693952, 2882303761517117440, 3458764513820540928, 4323455642275676160, 4611686018427387904, 5764607523034234880, 6917529027641081856, 8646911284551352320, 9223372036854775808, 11529215046068469760, 13835058055282163712, 17293822569102704640, 18446744073709551616
77760의 약수 중에서 가장 큰 약수는 18446744073709551616입니다.
따라서, 만들 수 있는 정육면체의 개수는 18446744073709551616개입니다.