Number System

(Number System)
1. State Euclid’s Division Lemma.
2. What is the HCF of 84 and 270?
3. Why the number 4n, where n is a natural number, cannot end with 0?
4. Show without finding product 5 x 7 x 11 + 7 is a composite number?
5. Show without actual division 40/9 is a non terminating decimal?
6. Using Euclid’s division algorithm, find the HCF of 2160 and 3520.
7. Use Euclid’s division algorithm to show that any positive odd integer is of the
form 4q + 1 or 4q + 3, where q is some integer.
8. Four cloth pieces measuring 14 cm, 18 cm, 22 cm and 26 cm respectively are
to be cut into least number of pieces of equal length. What is the length of
each piece?
9. Write the condition to be satisfied by q so that a rational number p/q has a
terminating expression.
10. Prove that 3 - rot5 is an irrational number.
11. Show that any one of the numbers (n + 2), n and (n + 4) is divisible by 3.
12. Prove that  rootN is an irrational number.
13. If 793800 = 2^3 x 3 ^m x 5^ n x 7 ^2, find the value of m and n.
14. Explain why 5 x 11 x 17 + 17 is a composite number while 7 x 6 x 3 x 5 + 1 is
not a composite number.
15. Prove that no number of the type 4K + 2 can be a perfect square.