List of 5-limit factorizations

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This list includes prime factorizations and monzos of all numbers from 1 to 99999 which are divisible by 5, and not divisible by any larger prime number.

integer factorization monzo
5 5 [0 0 1⟩
10 2⋅5 [1 0 1⟩
15 3⋅5 [0 1 1⟩
20 2⋅2⋅5 [2 0 1⟩
25 5⋅5 [0 0 2⟩
30 2⋅3⋅5 [1 1 1⟩
40 2⋅2⋅2⋅5 [3 0 1⟩
45 3⋅3⋅5 [0 2 1⟩
50 2⋅5⋅5 [1 0 2⟩
60 2⋅2⋅3⋅5 [2 1 1⟩
75 3⋅5⋅5 [0 1 2⟩
80 2⋅2⋅2⋅2⋅5 [4 0 1⟩
90 2⋅3⋅3⋅5 [1 2 1⟩
100 2⋅2⋅5⋅5 [2 0 2⟩
120 2⋅2⋅2⋅3⋅5 [3 1 1⟩
125 5⋅5⋅5 [0 0 3⟩
135 3⋅3⋅3⋅5 [0 3 1⟩
150 2⋅3⋅5⋅5 [1 1 2⟩
160 2⋅2⋅2⋅2⋅2⋅5 [5 0 1⟩
180 2⋅2⋅3⋅3⋅5 [2 2 1⟩
200 2⋅2⋅2⋅5⋅5 [3 0 2⟩
225 3⋅3⋅5⋅5 [0 2 2⟩
240 2⋅2⋅2⋅2⋅3⋅5 [4 1 1⟩
250 2⋅5⋅5⋅5 [1 0 3⟩
270 2⋅3⋅3⋅3⋅5 [1 3 1⟩
300 2⋅2⋅3⋅5⋅5 [2 1 2⟩
320 2⋅2⋅2⋅2⋅2⋅2⋅5 [6 0 1⟩
360 2⋅2⋅2⋅3⋅3⋅5 [3 2 1⟩
375 3⋅5⋅5⋅5 [0 1 3⟩
400 2⋅2⋅2⋅2⋅5⋅5 [4 0 2⟩
405 3⋅3⋅3⋅3⋅5 [0 4 1⟩
450 2⋅3⋅3⋅5⋅5 [1 2 2⟩
480 2⋅2⋅2⋅2⋅2⋅3⋅5 [5 1 1⟩
500 2⋅2⋅5⋅5⋅5 [2 0 3⟩
540 2⋅2⋅3⋅3⋅3⋅5 [2 3 1⟩
600 2⋅2⋅2⋅3⋅5⋅5 [3 1 2⟩
625 5⋅5⋅5⋅5 [0 0 4⟩
640 2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [7 0 1⟩
675 3⋅3⋅3⋅5⋅5 [0 3 2⟩
720 2⋅2⋅2⋅2⋅3⋅3⋅5 [4 2 1⟩
750 2⋅3⋅5⋅5⋅5 [1 1 3⟩
800 2⋅2⋅2⋅2⋅2⋅5⋅5 [5 0 2⟩
810 2⋅3⋅3⋅3⋅3⋅5 [1 4 1⟩
900 2⋅2⋅3⋅3⋅5⋅5 [2 2 2⟩
960 2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [6 1 1⟩
1000 2⋅2⋅2⋅5⋅5⋅5 [3 0 3⟩
1080 2⋅2⋅2⋅3⋅3⋅3⋅5 [3 3 1⟩
1125 3⋅3⋅5⋅5⋅5 [0 2 3⟩
1200 2⋅2⋅2⋅2⋅3⋅5⋅5 [4 1 2⟩
1215 3⋅3⋅3⋅3⋅3⋅5 [0 5 1⟩
1250 2⋅5⋅5⋅5⋅5 [1 0 4⟩
1280 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [8 0 1⟩
1350 2⋅3⋅3⋅3⋅5⋅5 [1 3 2⟩
1440 2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [5 2 1⟩
1500 2⋅2⋅3⋅5⋅5⋅5 [2 1 3⟩
1600 2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [6 0 2⟩
1620 2⋅2⋅3⋅3⋅3⋅3⋅5 [2 4 1⟩
1800 2⋅2⋅2⋅3⋅3⋅5⋅5 [3 2 2⟩
1875 3⋅5⋅5⋅5⋅5 [0 1 4⟩
1920 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [7 1 1⟩
2000 2⋅2⋅2⋅2⋅5⋅5⋅5 [4 0 3⟩
2025 3⋅3⋅3⋅3⋅5⋅5 [0 4 2⟩
2160 2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [4 3 1⟩
2250 2⋅3⋅3⋅5⋅5⋅5 [1 2 3⟩
2400 2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [5 1 2⟩
2430 2⋅3⋅3⋅3⋅3⋅3⋅5 [1 5 1⟩
2500 2⋅2⋅5⋅5⋅5⋅5 [2 0 4⟩
2560 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [9 0 1⟩
2700 2⋅2⋅3⋅3⋅3⋅5⋅5 [2 3 2⟩
2880 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [6 2 1⟩
3000 2⋅2⋅2⋅3⋅5⋅5⋅5 [3 1 3⟩
3125 5⋅5⋅5⋅5⋅5 [0 0 5⟩
3200 2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [7 0 2⟩
3240 2⋅2⋅2⋅3⋅3⋅3⋅3⋅5 [3 4 1⟩
3375 3⋅3⋅3⋅5⋅5⋅5 [0 3 3⟩
3600 2⋅2⋅2⋅2⋅3⋅3⋅5⋅5 [4 2 2⟩
3645 3⋅3⋅3⋅3⋅3⋅3⋅5 [0 6 1⟩
3750 2⋅3⋅5⋅5⋅5⋅5 [1 1 4⟩
3840 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [8 1 1⟩
4000 2⋅2⋅2⋅2⋅2⋅5⋅5⋅5 [5 0 3⟩
4050 2⋅3⋅3⋅3⋅3⋅5⋅5 [1 4 2⟩
4320 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [5 3 1⟩
4500 2⋅2⋅3⋅3⋅5⋅5⋅5 [2 2 3⟩
4800 2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [6 1 2⟩
4860 2⋅2⋅3⋅3⋅3⋅3⋅3⋅5 [2 5 1⟩
5000 2⋅2⋅2⋅5⋅5⋅5⋅5 [3 0 4⟩
5120 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [10 0 1⟩
5400 2⋅2⋅2⋅3⋅3⋅3⋅5⋅5 [3 3 2⟩
5625 3⋅3⋅5⋅5⋅5⋅5 [0 2 4⟩
5760 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [7 2 1⟩
6000 2⋅2⋅2⋅2⋅3⋅5⋅5⋅5 [4 1 3⟩
6075 3⋅3⋅3⋅3⋅3⋅5⋅5 [0 5 2⟩
6250 2⋅5⋅5⋅5⋅5⋅5 [1 0 5⟩
6400 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [8 0 2⟩
6480 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5 [4 4 1⟩
6750 2⋅3⋅3⋅3⋅5⋅5⋅5 [1 3 3⟩
7200 2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5 [5 2 2⟩
7290 2⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [1 6 1⟩
7500 2⋅2⋅3⋅5⋅5⋅5⋅5 [2 1 4⟩
7680 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [9 1 1⟩
8000 2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5 [6 0 3⟩
8100 2⋅2⋅3⋅3⋅3⋅3⋅5⋅5 [2 4 2⟩
8640 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [6 3 1⟩
9000 2⋅2⋅2⋅3⋅3⋅5⋅5⋅5 [3 2 3⟩
9375 3⋅5⋅5⋅5⋅5⋅5 [0 1 5⟩
9600 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [7 1 2⟩
9720 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5 [3 5 1⟩
10000 2⋅2⋅2⋅2⋅5⋅5⋅5⋅5 [4 0 4⟩
10125 3⋅3⋅3⋅3⋅5⋅5⋅5 [0 4 3⟩
10240 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [11 0 1⟩
10800 2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5 [4 3 2⟩
10935 3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [0 7 1⟩
11250 2⋅3⋅3⋅5⋅5⋅5⋅5 [1 2 4⟩
11520 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [8 2 1⟩
12000 2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5 [5 1 3⟩
12150 2⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [1 5 2⟩
12500 2⋅2⋅5⋅5⋅5⋅5⋅5 [2 0 5⟩
12800 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [9 0 2⟩
12960 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5 [5 4 1⟩
13500 2⋅2⋅3⋅3⋅3⋅5⋅5⋅5 [2 3 3⟩
14400 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5 [6 2 2⟩
14580 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [2 6 1⟩
15000 2⋅2⋅2⋅3⋅5⋅5⋅5⋅5 [3 1 4⟩
15360 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [10 1 1⟩
15625 5⋅5⋅5⋅5⋅5⋅5 [0 0 6⟩
16000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5 [7 0 3⟩
16200 2⋅2⋅2⋅3⋅3⋅3⋅3⋅5⋅5 [3 4 2⟩
16875 3⋅3⋅3⋅5⋅5⋅5⋅5 [0 3 4⟩
17280 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [7 3 1⟩
18000 2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅5 [4 2 3⟩
18225 3⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [0 6 2⟩
18750 2⋅3⋅5⋅5⋅5⋅5⋅5 [1 1 5⟩
19200 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [8 1 2⟩
19440 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5 [4 5 1⟩
20000 2⋅2⋅2⋅2⋅2⋅5⋅5⋅5⋅5 [5 0 4⟩
20250 2⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [1 4 3⟩
20480 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [12 0 1⟩
21600 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5 [5 3 2⟩
21870 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [1 7 1⟩
22500 2⋅2⋅3⋅3⋅5⋅5⋅5⋅5 [2 2 4⟩
23040 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [9 2 1⟩
24000 2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5 [6 1 3⟩
24300 2⋅2⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [2 5 2⟩
25000 2⋅2⋅2⋅5⋅5⋅5⋅5⋅5 [3 0 5⟩
25600 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [10 0 2⟩
25920 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5 [6 4 1⟩
27000 2⋅2⋅2⋅3⋅3⋅3⋅5⋅5⋅5 [3 3 3⟩
28125 3⋅3⋅5⋅5⋅5⋅5⋅5 [0 2 5⟩
28800 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5 [7 2 2⟩
29160 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [3 6 1⟩
30000 2⋅2⋅2⋅2⋅3⋅5⋅5⋅5⋅5 [4 1 4⟩
30375 3⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [0 5 3⟩
30720 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [11 1 1⟩
31250 2⋅5⋅5⋅5⋅5⋅5⋅5 [1 0 6⟩
32000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5 [8 0 3⟩
32400 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5⋅5 [4 4 2⟩
32805 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [0 8 1⟩
33750 2⋅3⋅3⋅3⋅5⋅5⋅5⋅5 [1 3 4⟩
34560 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [8 3 1⟩
36000 2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅5 [5 2 3⟩
36450 2⋅3⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [1 6 2⟩
37500 2⋅2⋅3⋅5⋅5⋅5⋅5⋅5 [2 1 5⟩
38400 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [9 1 2⟩
38880 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5 [5 5 1⟩
40000 2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5⋅5 [6 0 4⟩
40500 2⋅2⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [2 4 3⟩
40960 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [13 0 1⟩
43200 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5 [6 3 2⟩
43740 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [2 7 1⟩
45000 2⋅2⋅2⋅3⋅3⋅5⋅5⋅5⋅5 [3 2 4⟩
46080 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [10 2 1⟩
46875 3⋅5⋅5⋅5⋅5⋅5⋅5 [0 1 6⟩
48000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5 [7 1 3⟩
48600 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [3 5 2⟩
50000 2⋅2⋅2⋅2⋅5⋅5⋅5⋅5⋅5 [4 0 5⟩
50625 3⋅3⋅3⋅3⋅5⋅5⋅5⋅5 [0 4 4⟩
51200 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5 [11 0 2⟩
51840 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5 [7 4 1⟩
54000 2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5⋅5 [4 3 3⟩
54675 3⋅3⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [0 7 2⟩
56250 2⋅3⋅3⋅5⋅5⋅5⋅5⋅5 [1 2 5⟩
57600 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5 [8 2 2⟩
58320 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [4 6 1⟩
60000 2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5⋅5 [5 1 4⟩
60750 2⋅3⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [1 5 3⟩
61440 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5 [12 1 1⟩
62500 2⋅2⋅5⋅5⋅5⋅5⋅5⋅5 [2 0 6⟩
64000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5 [9 0 3⟩
64800 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅5⋅5 [5 4 2⟩
65610 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [1 8 1⟩
67500 2⋅2⋅3⋅3⋅3⋅5⋅5⋅5⋅5 [2 3 4⟩
69120 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5 [9 3 1⟩
72000 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅5 [6 2 3⟩
72900 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [2 6 2⟩
75000 2⋅2⋅2⋅3⋅5⋅5⋅5⋅5⋅5 [3 1 5⟩
76800 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5 [10 1 2⟩
77760 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5 [6 5 1⟩
78125 5⋅5⋅5⋅5⋅5⋅5⋅5 [0 0 7⟩
80000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅5⋅5⋅5⋅5 [7 0 4⟩
81000 2⋅2⋅2⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [3 4 3⟩
81920 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅5 [14 0 1⟩
84375 3⋅3⋅3⋅5⋅5⋅5⋅5⋅5 [0 3 5⟩
86400 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅5⋅5 [7 3 2⟩
87480 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [3 7 1⟩
90000 2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅5⋅5 [4 2 4⟩
91125 3⋅3⋅3⋅3⋅3⋅3⋅5⋅5⋅5 [0 6 3⟩
92160 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅5 [11 2 1⟩
93750 2⋅3⋅5⋅5⋅5⋅5⋅5⋅5 [1 1 6⟩
96000 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅5⋅5⋅5 [8 1 3⟩
97200 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅5⋅5 [4 5 2⟩
98415 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅5 [0 9 1⟩


Icon-Todo.png Todo: clarify, improve synopsis
Explain the musical uses for this table in the introduction.
Icon-Todo.png Todo: link
Link to this table from relevant pages, and add a see also at the end to give readers somewhere to go next.
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