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- Thread starter ak730
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Yes, it's called "prime factorization":Hi,

Not sure if Im explaining correctly.

Is there a formula or way to calculate which numbers we can divide a certain number to only produce non decimal numbers?

For example:

466

Only 2 and 233 will produce a non decimal number.

[imath]466 = 2 \cdot 233[/imath]

So 466 can only be divided "evenly" by the primes 2 and 233 (ie. without any extra decimals.)

A more illuminating example would be [imath]180 = 2^2 \cdot 3^2 \cdot 5[/imath]. 180 can be divided evenly by any combination of two 2's, two 3's and a 5:

[imath]2, 3, 2^2, 5, 2 \cdot 3, 3^2, 2 \cdot 5, 2^2 \cdot 3, 3 \cdot 5, 2 \cdot 3^2, 2^2 \cdot 5, 2 \cdot 3 \cdot 5, 2^2 \cdot 3^2, 3^2 \cdot 5, 2 \cdot 3^2 \cdot 5, 2^2 \cdot 3^2 \cdot 5[/imath]

or 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.

-Dan

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What you're asking for is the "Hi,

Not sure if Im explaining correctly.

Is there a formula or way to calculate whichnumbers we can divide a certain number to only produce non decimal numbers?

For example:

466

Only 2 and 233 will produce a non decimal number.

There is no simple "formula", but once you have found the

Now that you have words for what you want, you should be able to search for fuller explanations of these ideas.

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The easiest way to answer is by way of example.Not sure if Im explaining correctly.Is there a formula or way to calculate which numbers we can divide a certain number to only produce non decimal numbers?

For example: 466 Only 2 and 233 will produce a non decimal number.

That tell us that there are [imath]420[/imath] positive integral factors of [imath]19,132,858,800[/imath]

If you work out why that works you will understand your own question.

[imath][/imath][imath][/imath]

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For the record 466/1 and 466/466 will also be non decimal numbers.Hi,

Not sure if Im explaining correctly.

Is there a formula or way to calculate which numbers we can divide a certain number to only produce non decimal numbers?

For example:

466

Only 2 and 233 will produce a non decimal number.

466/1 = 466.0000000For the record 466/1 and 466/466 will also benon decimal numbers.

466/466 = 1.0000000

I think there is a confusion about the definition of "non-decimal number". A better classification would be non-recurring decimal - as in π) or recurring decimal (as in 4/33 = 0.121212...)

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