CT 3: Rules of Divisibility

1.Which of the following is the smallest 5 -digits number that is exactly divisible by 526?

2. Which of the following numbers is NOT divisible by 11?

3. What is the remainder when (x¹⁷ + 1) is divided by (x + 1)?

4. Which is the smallest 5-digit number that is divisible by each of 54, 120 and 96? 

5. A number when divided by a divisor leaves a remainder of 25. When twice the original number is divided by the same divisor, the remainder is 13. What is the value of the divisor?

6. The total number of three digit numbers divisible by 3 or 5 is ____.

7. Which number among 34623, 34716, 34782 and 34783 is NOT divisible by 3? 

8. When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is: 

9. What is the least natural number that should be added to 1135 so that the sum is completely divisible by 3, 4, 5, and 6?

10. An 11-digit number 7823326867X is divisible by 18. What is the value of X?