1. The problem is to find $23 \bmod 7$, which means finding the remainder when 23 is divided by 7. 2. The formula for modular arithmetic is: $$a \bmod n = r$$ where $a$ is the number, $n$ is the modulus, and $r$ is the remainder when $a$ is divided by $n$. 3. Divide 23 by 7: $$23 \div 7 = 3 \text{ remainder } r$$ 4. Calculate the product of the quotient and the modulus: $$3 \times 7 = 21$$ 5. Subtract this product from the original number to find the remainder: $$23 - 21 = 2$$ 6. Therefore: $$23 \bmod 7 = 2$$ The remainder when 23 is divided by 7 is 2.