1. The problem is to find the remainder when 511 is divided by 8. 2. To find the remainder, we use the division algorithm: $$\text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}$$ 3. Divide 511 by 8: $$511 \div 8 = 63 \text{ remainder } r$$ 4. Calculate the quotient: $$8 \times 63 = 504$$ 5. Find the remainder: $$r = 511 - 504 = 7$$ 6. Therefore, the remainder when 511 is divided by 8 is $7$. This means $511 = 8 \times 63 + 7$. Note: The second expression involving 126 and 4 is not solved as per instructions to solve only the first problem.