Class X : HOTS Question Answers: Math Unit - 1 (Number system)
Numbers are intellectual witnesses that belong only to
1. If the H C F of 657 and 963 is expressible in the form of
657x + 963x - 15 find x.
2. Express the GCD of 48 and 18 as a linear combination.
(Ans: Not unique)
3. Prove that one of every three consecutive integers is
divisible by 3.
4. Find the largest possible positive integer that will
divide 398, 436, and 542 leaving remainder 7, 11, 15 respectively. (Ans: 17)
5. Find the least number that is divisible by all numbers
between 1 and 10 (both inclusive).
6. Show that 571 is a prime number.
7. If d is the HCF of 30, 72, find the value of x & y
satisfying d = 30x + 72y.
8. Show that the product of 3 consecutive positive integers
is divisible by 6.
9. Show that for odd positive integer to be a perfect square,
it should be of the form
10. Find the greatest number of 6 digits exactly divisible by
24, 15 and 36. (Ans:999720)