Common Modulo Patterns

You'll see these patterns repeatedly:

$\bullet$ Checking divisibility: $a \bmod b = 0$ means $b$ divides $a$

$\bullet$ Extracting last digit: $n \bmod 10$

$\bullet$ Cycling indices: $i \bmod n$ wraps $i$ to range $[0, n-1]$

$\bullet$ Preventing overflow: apply modulo at each step in calculations

$\bullet$ Hash functions: $\text{hash}(x) = x \bmod m$ distributes values into $m$ buckets