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.
Yes, it's called "prime factorization":
[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