Can a large number be shrunk (data size) without losing information

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So right now I'm just messing around with some stuff using a ti-84 calculator but the issue is the numbers I'm playing with get really big really fast and eventually I get an overflow error. Is there anyway I can shrink the numbers down without losing their factors? Or is the impossible

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If you care about factors, no, depending on the calculations you want to do. The most common way to handle large numbers is scientific notation, which your calculator supports. It only stores a certain precision, so if you want to determine the factors of $123456789123456987$ you are out of luck. That has a factor $9$, but $123456789123456988$ does not and I suspect the calculator cannot tell the difference. For some computations you can take the modulus often enough to keep the numbers within range. There are also (I suspect not on the calculator) packages like Wolfram Alpha that have arbitrary precision.