Table of 3-limit factorizations

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This table 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⟩

See also