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Many people have spent a significant amount of time on a proof for this, but here's the most straghtforward proof I can think of:

When you devide any number, you are dividing the number into units that are as big as you specify. For example, 10 / 2 divides ten into groups of 2. You'll end up with 5 groups, so 5 is the answer.

If you devide any number into groups of 1, you will end up with the same number.

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Q: Why whenever a number divided by itself equal to 1?
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Any non-zero number divided by itself is equal to one.


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