How can I mathematically split up a 3 digit number?

You can use the operation "modulo". It calculates the remainder after you have divided by a number.

1. So 456 modulo 10 is 6, now you have the first digit.
2. Then you can divide 456 with 10 without remainder, you get 45.
3. Now 45 modulo 10 gives 5, now you have second digit.
4. Then you can divide 45 with 10 without remainder, you get 4.
5. Now 4 modulo 10 gives 4, now you have last digit.

Divide $456$ with $100$ without remainder, you get $4$ - the first digit

Now $456 - 4\cdot100 = 56$ - subtract $100$ times the first digit

Now divide $56$ with $10$ without remainder to get 5 - the second digit

Now do $56 - 5\cdot10 = 6$ - last digit

You can use $\mod{}$ to get them another way, from last (or first if you call it that way) to first digit