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When you add two multiples of a certain number together, the sum will also be a multiple of that number. This is true for subtraction as well. For example, imagine we do the following:
$$13+26=39$$
Notice that $13$ and $26$ are both multiples of $13$. Also notice that the sum $39$ is ALSO a multiple of $13$. This might seem pretty obvious but it can be pretty tricky.
Tricky Example
Is the sum below prime or not prime? How do you know?
$$30! + 29$$
We know that $30!$ is a multiple of $29$. We also know that $29$ is a multiple of $29$. So we're adding two multiples of $29$ together, giving us a sum that is a multiple of $29$ greater than $29$. Thus, we can confidently say that this sum is not prime, even though the number is stupidly large.