1. Use Euclid’s division algorithm to find the HCF of 867 and 255
2. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
3. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9lm + 1 or 9m + 8.
4. Prove that 7 √5 is irrational.
5. Prove that √5 is irrational.
6. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
7. Express 5005 as a product of its prime factors.
8. Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.
9. Find the LCM and HCF of 96 and 404 by the prime factorization method
10. State whether 64/455 will have a terminating decimal expansion or a non-terminating repeating decimal
11. State whether15/ 1600 will have a terminating decimal expansion or a non-terminating repeating decimal.
12. Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers.
13. Use Euclid’s division algorithm to find the HCF of 196 and 38220 (3 marks)
14. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9m + 1 or 9m + 8
15. Show that every positive odd integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer
2. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
3. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9lm + 1 or 9m + 8.
4. Prove that 7 √5 is irrational.
5. Prove that √5 is irrational.
6. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
7. Express 5005 as a product of its prime factors.
8. Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.
9. Find the LCM and HCF of 96 and 404 by the prime factorization method
10. State whether 64/455 will have a terminating decimal expansion or a non-terminating repeating decimal
11. State whether15/ 1600 will have a terminating decimal expansion or a non-terminating repeating decimal.
12. Find the LCM and HCF of 510 and 92 and verify that LCM × HCF = product of the two numbers.
13. Use Euclid’s division algorithm to find the HCF of 196 and 38220 (3 marks)
14. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9m + 1 or 9m + 8
15. Show that every positive odd integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer
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