Question

A number is formed by writing first 54 natural numbers in front of each other as 12345678910111213... Find the remainder when this number is divided by 8.

• A. 1
• B. 7
• C. 2
• D. 0

Hint:

For divisibility by 8, you can simply focus on the last three digits of the number instead of the entire number.

Answer 1

The Correct Option is C

We need to find the remainder when a large number formed by writing the first 54 natural numbers in front of each other is divided by 8. Instead of dealing with the entire number, we can use the divisibility rule for 8. The rule for divisibility by 8 states that a number is divisible by 8 if the last three digits of the number are divisible by 8. Let's look at the last three digits of the number formed by writing the first 54 numbers: - The first 54 numbers are 1, 2, 3, ..., 54, so the number ends with the digits "543". Now, divide 543 by 8: \[ 543 \div 8 = 67 \text{ remainder } 7. \] Thus, the remainder when this large number is divided by 8 is 7.