Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 164 · 40 questions

How to solve it (Factors come in pairs): Find factors in pairs: 1 × N, 2 × …, 3 × …, until the pairs meet. Prime factorisation: keep dividing by the smallest prime that works, then group equal primes as powers. 1 is not a prime; 2 is the only even prime. To test a number, try dividing by the primes up to its square root.

1. 1.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
2. 2.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 5 (d) 7
3. 3.How many factors does 95 have? (a) 3 (b) 4 (c) 2 (d) 5
4. 4.How many factors does 31 have? (a) 2 (b) 3 (c) 1 (d) 4
5. 5.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
6. 6.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
7. 7.What is the prime factorisation of 84? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
8. 8.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
9. 9.How many prime numbers are there between 30 and 40? (a) 3 (b) 4 (c) 1 (d) 2
10. 10.What is the smallest prime factor of 299? (a) 1 (b) 23 (c) 13 (d) 2
11. 11.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2 × 5² (d) 2³ × 5
12. 12.How many factors does 89 have? (a) 3 (b) 2 (c) 4 (d) 1
13. 13.How many factors does 18 have? (a) 6 (b) 5 (c) 7 (d) 4
14. 14.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2⁵ × 3
15. 15.How many prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 6 (d) 8
16. 16.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2² × 5 × 7
17. 17.How many factors does 80 have? (a) 8 (b) 9 (c) 10 (d) 11
18. 18.How many prime numbers are there between 50 and 80? (a) 7 (b) 8 (c) 6 (d) 9
19. 19.How many factors does 70 have? (a) 6 (b) 7 (c) 9 (d) 8
20. 20.How many factors does 34 have? (a) 3 (b) 2 (c) 5 (d) 4
21. 21.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 1 (d) 2
22. 22.How many factors does 107 have? (a) 4 (b) 3 (c) 2 (d) 1
23. 23.What is the smallest prime factor of 35? (a) 5 (b) 1 (c) 2 (d) 7
24. 24.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 7 (d) 6
25. 25.What is the smallest prime factor of 51? (a) 1 (b) 2 (c) 3 (d) 17
26. 26.How many prime numbers are there between 50 and 60? (a) 2 (b) 1 (c) 3 (d) 4
27. 27.How many factors does 15 have? (a) 5 (b) 2 (c) 4 (d) 3
28. 28.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 2 (d) 1
29. 29.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7 (d) 3 × 7²
30. 30.How many factors does 39 have? (a) 4 (b) 3 (c) 5 (d) 2
31. 31.How many prime numbers are there between 60 and 90? (a) 8 (b) 6 (c) 9 (d) 7
32. 32.How many factors does 114 have? (a) 8 (b) 6 (c) 9 (d) 7
33. 33.What is the prime factorisation of 28? (a) 2 × 7² (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7
34. 34.How many prime numbers are there between 40 and 70? (a) 9 (b) 7 (c) 8 (d) 6
35. 35.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3 × 5 × 7 (d) 3² × 5 × 7
36. 36.How many factors does 55 have? (a) 2 (b) 5 (c) 4 (d) 3
37. 37.How many factors does 68 have? (a) 6 (b) 7 (c) 4 (d) 5
38. 38.How many prime numbers are there between 70 and 90? (a) 4 (b) 5 (c) 7 (d) 6
39. 39.How many factors does 12 have? (a) 7 (b) 4 (c) 6 (d) 5
40. 40.How many prime numbers are there between 80 and 90? (a) 1 (b) 3 (c) 4 (d) 2

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad