List of 3-limit factorizations: Difference between revisions
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This list includes prime factorizations and [[monzo]]s of all numbers from 1 to | This list includes prime factorizations and [[monzo]]s of all numbers from 1 to 9999999 (10<sup>7</sup>-1) which are divisible by 3, and not divisible by any larger [[prime number]]. | ||
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| 995328 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 5 }} | | 995328 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 5 }} | ||
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| 1062882 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 12 }} | |||
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| 1119744 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 9 7 }} | |||
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| 1179648 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 17 2 }} | |||
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| 1259712 || 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 6 9 }} | |||
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| 1327104 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 14 4 }} | |||
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| 1417176 || 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 3 11 }} | |||
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| 1492992 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 11 6 }} | |||
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| 1572864 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 19 1 }} | |||
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| 1594323 || 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 0 13 }} | |||
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| 1679616 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 8 8 }} | |||
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| 1769472 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 16 3 }} | |||
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| 1889568 || 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 5 10 }} | |||
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| 1990656 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 13 5 }} | |||
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| 2125764 || 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 2 12 }} | |||
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| 2239488 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 10 7 }} | |||
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| 2359296 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 18 2 }} | |||
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| 2519424 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 7 9 }} | |||
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| 2654208 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 15 4 }} | |||
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| 2834352 || 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 4 11 }} | |||
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| 2985984 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 6 }} | |||
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| 3145728 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 20 1 }} | |||
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| 3188646 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 13 }} | |||
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| 3359232 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 9 8 }} | |||
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| 3538944 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 17 3 }} | |||
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| 3779136 || 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 6 10 }} | |||
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| 3981312 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 14 5 }} | |||
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| 4251528 || 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 3 12 }} | |||
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| 4478976 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 11 7 }} | |||
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| 4718592 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 19 2 }} | |||
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| 4782969 || 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 0 14 }} | |||
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| 5038848 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 8 9 }} | |||
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| 5308416 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 16 4 }} | |||
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| 5668704 || 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 5 11 }} | |||
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| 5971968 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 13 6 }} | |||
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| 6291456 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 21 1 }} | |||
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| 6377292 || 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 2 13 }} | |||
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| 6718464 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 10 8 }} | |||
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| 7077888 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 18 3 }} | |||
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| 7558272 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 7 10 }} | |||
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| 7962624 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 15 5 }} | |||
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| 8503056 || 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 4 12 }} | |||
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| 8957952 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 7 }} | |||
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| 9437184 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 20 2 }} | |||
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| 9565938 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 14 }} | |||
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{{todo|inline=1|clarify|improve synopsis|comment=Explain the musical uses for this table in the introduction.}} | |||
{{todo|inline=1|link|comment=Link to this table from relevant pages, and add a see also at the end to give readers somewhere to go next.}} | |||
[[Category:3-limit]] | |||
[[Category:Math]] | |||
[[Category:Lists]] |