Q. 1. If the H C F of 657 and 963 is expressible in the form of 657x + 963x - 15 find x.
Q. 2. Express the GCD of 48 and 18 as a linear combination.
Q. 3. Prove that one of every three consecutive integers is divisible by 3.
Q. 4. Find the largest possible positive integer that will divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively.
Q. 5. Find the least number that is divisible by all numbers between 1 and 10 (both inclusive).
Q. 6. Show that 571 is a prime number.
Q. 7. If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y.
Q. 8. Show that the product of 3 consecutive positive integers is divisible by 6.
Q. 9. Show that for odd positive integer to be a perfect square, it should be of the form 8k +1. Let a=2m+1
Q. 10. Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.
Q. 11. If a and b are positive integers. Show that √2 always lies between a/b and a-2b/a+b
Q. 12. Prove that ( √n-1+ √n +1 ) is irrational, for every n 
N n-1 is totally in square root .
