When the number 3521 is divided by 8, what is the remainder?

Introduction / Context:
This question is about finding the remainder when a large number is divided by 8. It reinforces the idea that to test divisibility by 8 or to find the remainder, you only need to look at the last three digits of the number, because 1000 is divisible by 8.

Given Data / Assumptions:

- The number given is 3521.

- We are dividing this number by 8.

- We must find the remainder after division.

Concept / Approach:
A number is divisible by 8 if the integer formed by its last three digits is divisible by 8. Similarly, the remainder when the whole number is divided by 8 is the same as the remainder when the last three digits are divided by 8. This is because 1000, 2000, etc. are multiples of 8.

Step-by-Step Solution:
Step 1: Extract the last three digits of 3521. The last three digits are 521. Step 2: Divide 521 by 8 and find the remainder. 8 × 65 = 520. 521 - 520 = 1. So the remainder when 521 is divided by 8 is 1. Step 3: Conclude for the whole number 3521. Since the remainder for the last three digits is 1, the remainder when 3521 is divided by 8 is also 1.

Verification / Alternative check:
Alternatively, perform the full division roughly: 8 × 400 = 3200. 3521 - 3200 = 321. 8 × 40 = 320. 321 - 320 = 1. We again obtain a remainder of 1, confirming our earlier result based on the last three digits.

Why Other Options Are Wrong:
- 3, 7, 9: These are simply incorrect remainders; detailed division shows the remainder must be 1. None of them is compatible with the exact calculations above.

Common Pitfalls:
Some students try to divide the entire number step by step without using the three digit shortcut, which increases the chance of arithmetic mistakes. Others confuse the divisibility rule for 4 (using last two digits) with that for 8 (using last three digits). Remember that powers of 10 and their divisibility by 8 explain why only the last three digits matter.

Final Answer:
The remainder when 3521 is divided by 8 is 1.