Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 142 · 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 smallest prime factor of 161? (a) 7 (b) 23 (c) 1 (d) 2
2. 2.How many prime numbers are there between 70 and 90? (a) 6 (b) 5 (c) 4 (d) 7
3. 3.How many prime numbers are there between 20 and 50? (a) 7 (b) 8 (c) 6 (d) 9
4. 4.How many factors does 81 have? (a) 6 (b) 5 (c) 3 (d) 4
5. 5.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 2 (d) 3
6. 6.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 2 (d) 7
7. 7.How many factors does 119 have? (a) 5 (b) 4 (c) 2 (d) 3
8. 8.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2³ × 3² × 5
9. 9.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 2 (d) 11
10. 10.How many factors does 12 have? (a) 6 (b) 7 (c) 4 (d) 5
11. 11.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2 × 3² (c) 2² × 3 (d) 2² × 3²
12. 12.How many prime numbers are there between 30 and 40? (a) 2 (b) 4 (c) 3 (d) 1
13. 13.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
14. 14.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 1 (d) 13
15. 15.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 5 (d) 4
16. 16.How many prime numbers are there between 40 and 60? (a) 6 (b) 4 (c) 7 (d) 5
17. 17.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
18. 18.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 1 (d) 3
19. 19.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2⁵ × 5 × 7
20. 20.How many factors does 32 have? (a) 7 (b) 4 (c) 6 (d) 5
21. 21.How many factors does 83 have? (a) 2 (b) 3 (c) 4 (d) 1
22. 22.How many factors does 79 have? (a) 2 (b) 1 (c) 4 (d) 3
23. 23.How many factors does 24 have? (a) 7 (b) 9 (c) 6 (d) 8
24. 24.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 7 (d) 5
25. 25.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
26. 26.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
27. 27.How many factors does 88 have? (a) 8 (b) 7 (c) 9 (d) 6
28. 28.What is the smallest prime factor of 187? (a) 11 (b) 17 (c) 2 (d) 1
29. 29.What is the prime factorisation of 28? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
30. 30.How many factors does 16 have? (a) 5 (b) 3 (c) 4 (d) 6
31. 31.What is the smallest prime factor of 319? (a) 29 (b) 11 (c) 2 (d) 1
32. 32.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 1 (d) 23
33. 33.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 7 (d) 6
34. 34.How many factors does 104 have? (a) 9 (b) 8 (c) 7 (d) 6
35. 35.What is the smallest prime factor of 21? (a) 1 (b) 7 (c) 3 (d) 2
36. 36.How many prime numbers are there between 90 and 100? (a) 3 (b) 0 (c) 1 (d) 2
37. 37.What is the prime factorisation of 36? (a) 2² × 3² (b) 2³ × 3² (c) 2 × 3² (d) 2² × 3³
38. 38.How many factors does 97 have? (a) 2 (b) 3 (c) 1 (d) 4
39. 39.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 7 (d) 5
40. 40.How many factors does 73 have? (a) 1 (b) 3 (c) 2 (d) 4

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