Find the remainder when 629 is divided by 8.

Introduction / Context:
This is a straightforward remainder problem that tests your ability to perform division and understand how to extract the remainder. Questions of this type are basic but essential for number system and modular arithmetic topics.

Given Data / Assumptions:

• We have the integer 629.
• We divide 629 by 8.
• We must find the remainder when this division is performed.

Concept / Approach:
The remainder r when a number N is divided by d is the amount left after subtracting the largest multiple of d not exceeding N. Formally, N = dq + r where 0 ≤ r < d. We can find r either by long division or by recognising nearby multiples of 8.

Step-by-Step Solution:
Step 1: Find the nearest multiple of 8 less than or equal to 629.Step 2: Since 8 * 78 = 624 and 8 * 79 = 632, which is greater than 629, we use 624.Step 3: Compute the difference: 629 - 624 = 5.Step 4: By the division algorithm, 629 = 8 * 78 + 5, so the quotient is 78 and the remainder is 5.

Verification / Alternative check:
Perform a quick long division of 629 by 8. You will again obtain 78 as the quotient and see that 8 multiplied by 78 gives 624, leaving 5 as the remainder.Since 5 is less than 8, it is a valid remainder.

Why Other Options Are Wrong:
0 would mean 629 is exactly divisible by 8, which is not true because 629 / 8 is not an integer.1 and 3 are remainders that arise from incorrect subtraction or choosing the wrong multiple of 8.

Common Pitfalls:
Choosing 632 as the multiple of 8 leads to a negative remainder, which is not allowed in standard remainder definition.Another error is miscalculating 8 * 78 or 8 * 79.Always pick the largest multiple of the divisor that does not exceed the dividend, then subtract accurately.

Final Answer:
The remainder when 629 is divided by 8 is 5.