Divisibility
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Divisibility
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21 Questions

1. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9.However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4.What is the value of the divisor?
2. If M183 is divisible by 11, find the value of the smallest natural number M ?
3. What is the value of M and N respectively if M39048458N is divisible by 8 and 11, where M and N are single digit integers?
4. 2ab5 is a four-digit number divisible by 25. If the number formed from the two digits ab is a multiple of 13, then ab=
5. Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8
6. A number is formed by writing first 67 natural numbers in front of each other as 34567891011.... What is the remainder when this number is divided by 8?
7. How many natural numbers below 660 are divisible by 5 and 11 but not by 3?
8. A number when divided by a divisor leaves a remainder of 24.When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
9. What is the smallest number which must be added to 8261955 so as to obtain a sum which is divisible by 11?
10. If each of the three nonzero numbers a, b and c is divisible by 3, then abc must be divisible by which one of the following the numbers?
11. Find the sum of the digits of the least natural number P, such that the sum of the cubes of the four smallest distinct divisors of P equals 2P.
12. What is the least value of x such that 7648x is divisible by 11?
13. The sum of three digit number is subtracted from the number. The Resulting number is always:
14. For a number to be divisible by 88 it should be:
15. Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8
16. A number is formed by writing first 67 natural numbers in front of each other as 34567891011.... What is the remainder when this number is divided by 8?
17. The sum of three digit number is subtracted from the number. The Resulting number is always:
18. When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9.However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4.What is the value of the divisor?
19. If M183 is divisible by 11, find the value of the smallest natural number M ?
20. What is the least value of x such that 7648x is divisible by 11?
21. Find the least of value of k so that the number 37k124 is divisible by 9 ?

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