List of 3-limit factorizations

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This list includes prime factorizations and monzos of all numbers from 1 to 9999999 (107-1) which are divisible by 3, and not divisible by any larger prime number.

integer factorization monzo
3 3 | 0 1 >
6 2⋅3 | 1 1 >
9 3⋅3 | 0 2 >
12 2⋅2⋅3 | 2 1 >
18 2⋅3⋅3 | 1 2 >
24 2⋅2⋅2⋅3 | 3 1 >
27 3⋅3⋅3 | 0 3 >
36 2⋅2⋅3⋅3 | 2 2 >
48 2⋅2⋅2⋅2⋅3 | 4 1 >
54 2⋅3⋅3⋅3 | 1 3 >
72 2⋅2⋅2⋅3⋅3 | 3 2 >
81 3⋅3⋅3⋅3 | 0 4 >
96 2⋅2⋅2⋅2⋅2⋅3 | 5 1 >
108 2⋅2⋅3⋅3⋅3 | 2 3 >
144 2⋅2⋅2⋅2⋅3⋅3 | 4 2 >
162 2⋅3⋅3⋅3⋅3 | 1 4 >
192 2⋅2⋅2⋅2⋅2⋅2⋅3 | 6 1 >
216 2⋅2⋅2⋅3⋅3⋅3 | 3 3 >
243 3⋅3⋅3⋅3⋅3 | 0 5 >
288 2⋅2⋅2⋅2⋅2⋅3⋅3 | 5 2 >
324 2⋅2⋅3⋅3⋅3⋅3 | 2 4 >
384 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 7 1 >
432 2⋅2⋅2⋅2⋅3⋅3⋅3 | 4 3 >
486 2⋅3⋅3⋅3⋅3⋅3 | 1 5 >
576 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 6 2 >
648 2⋅2⋅2⋅3⋅3⋅3⋅3 | 3 4 >
729 3⋅3⋅3⋅3⋅3⋅3 | 0 6 >
768 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 8 1 >
864 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 5 3 >
972 2⋅2⋅3⋅3⋅3⋅3⋅3 | 2 5 >
1152 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 7 2 >
1296 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 4 4 >
1458 2⋅3⋅3⋅3⋅3⋅3⋅3 | 1 6 >
1536 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 9 1 >
1728 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 6 3 >
1944 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 3 5 >
2187 3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 7 >
2304 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 8 2 >
2592 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 5 4 >
2916 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 2 6 >
3072 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 10 1 >
3456 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 7 3 >
3888 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 4 5 >
4374 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 7 >
4608 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 9 2 >
5184 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 6 4 >
5832 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 3 6 >
6144 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 11 1 >
6561 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 8 >
6912 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 8 3 >
7776 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 5 5 >
8748 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 7 >
9216 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 10 2 >
10368 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 7 4 >
11664 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 4 6 >
12288 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 12 1 >
13122 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 8 >
13824 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 9 3 >
15552 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 6 5 >
17496 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 7 >
18432 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 11 2 >
19683 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 9 >
20736 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 8 4 >
23328 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 5 6 >
24576 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 13 1 >
26244 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 8 >
27648 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 10 3 >
31104 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 7 5 >
34992 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 7 >
36864 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 12 2 >
39366 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 9 >
41472 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 9 4 >
46656 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 6 6 >
49152 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 14 1 >
52488 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 8 >
55296 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 11 3 >
59049 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 10 >
62208 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 8 5 >
69984 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 5 7 >
73728 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 13 2 >
78732 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 9 >
82944 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 10 4 >
93312 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 7 6 >
98304 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 15 1 >
104976 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 8 >
110592 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 12 3 >
118098 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 10 >
124416 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 9 5 >
139968 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 6 7 >
147456 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 14 2 >
157464 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 9 >
165888 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 11 4 >
177147 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 11 >
186624 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 8 6 >
196608 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 16 1 >
209952 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 5 8 >
221184 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 13 3 >
236196 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 10 >
248832 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 10 5 >
279936 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 7 7 >
294912 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 15 2 >
314928 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 9 >
331776 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 12 4 >
354294 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 11 >
373248 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 9 6 >
393216 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 17 1 >
419904 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 6 8 >
442368 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 14 3 >
472392 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 10 >
497664 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 11 5 >
531441 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 12 >
559872 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 8 7 >
589824 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 16 2 >
629856 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 5 9 >
663552 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 13 4 >
708588 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 11 >
746496 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 10 6 >
786432 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 18 1 >
839808 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 7 8 >
884736 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 15 3 >
944784 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 10 >
995328 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 12 5 >
1062882 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 12 >
1119744 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 9 7 >
1179648 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 17 2 >
1259712 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 6 9 >
1327104 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 14 4 >
1417176 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 11 >
1492992 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 11 6 >
1572864 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 19 1 >
1594323 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 13 >
1679616 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 8 8 >
1769472 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 16 3 >
1889568 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 5 10 >
1990656 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 13 5 >
2125764 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 12 >
2239488 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 10 7 >
2359296 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 18 2 >
2519424 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 7 9 >
2654208 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 15 4 >
2834352 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 11 >
2985984 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 12 6 >
3145728 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 20 1 >
3188646 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 13 >
3359232 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 9 8 >
3538944 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 17 3 >
3779136 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 6 10 >
3981312 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 14 5 >
4251528 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 3 12 >
4478976 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 11 7 >
4718592 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 19 2 >
4782969 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 0 14 >
5038848 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 8 9 >
5308416 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | 16 4 >
5668704 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 5 11 >
5971968 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | 13 6 >
6291456 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | 21 1 >
6377292 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 2 13 >
6718464 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 10 8 >
7077888 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | 18 3 >
7558272 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 7 10 >
7962624 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | 15 5 >
8503056 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 4 12 >
8957952 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 12 7 >
9437184 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | 20 2 >
9565938 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | 1 14 >