1. The HCF and product of two numbers are 15 and 6300 respectively. Find how many pairs of such numbers are possible.

2. If P713 is divisible by 11, find the value of the smallest natural number P?

3. Find the dividend if the divisor is (x + 2), quotient is (4x - 5) and the remainder is 12.

4. What is the value of 2 consecutive natural numbers, sum of whose squares is 145?

5. Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:

6. Find the greatest number that will divide 149, 247 and 622 leaving remainders 5, 7 and 10 respectively

7. Find the value of \(\frac{1}{4} + \frac{1} + \frac{1} + \frac{1} + \frac{1}\)

8. A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is

9. The LCM of two numbers is 210. lf their HCF is 35 and one of the numbers is 105, find the other number.

10. 351 + 352 + 353 + 354 is divisible by

11. The LCM of two numbers is 66. The numbers are in the ratio 2 : 3. The sum of the numbers is

12. Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:

13. How many 3 digit number, in all are divisible by 9?

14. The greatest 4-digit number exactly divisible by 5, 15, 20 is

15. Find the remainder when 413 divided by 3?

16. What is the greatest number less than 900, which is divisible by 8, 12 and 28?

17. Find the least number required to be added to 3105 so that it is exactly divisible by 3, 4, 5 and 6.

18. What smallest number should be added to the sum of squares of 15 and 14, so that the resulting number is a perfect square?

19. Find the LCM Of 25/7, 15/28, 20/21.

20. Which of the following will have the maximum number of factors?

21. If x = 3 + 2√2, the value of \({x^2} + \frac{1}}\) is

22. It is given that 237 + 1 is exactly divisible by a certain number. Which one of the following is definitely also divisible by the same number?

23. By dividing 14528 by a certain number, Suresh gets 83 as quotient and 3 as remainder. What is the divisor?

24. The HCF of 3/7, 5/14 and 17/28 is:

25. The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, the dividend is:

26. At a telephone exchange, three phones ring at intervals of 20 sec, 24 sec and 30 seconds - If they ring together at 11:25 am, when will they next ring together?

27. The HCF and LCM of the two numbers x and y are respectively 7 and 42. If x + y = 35, then \(\frac{1}{x} + \frac{1}{y}\) is equal to :

28. If x is a prime number, LCM of x and its successive number would be

29. What is the least number which when increased by 23 is divisible by each of 42, 36 and 45?

30. What is the L.C.M and H.C.F of the fractions \(\frac{6}{5},\frac{3}{5}{\text{and}}\frac?\)