Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 60 · 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.How many factors does 115 have? (a) 2 (b) 3 (c) 5 (d) 4
2. 2.How many prime numbers are there between 70 and 80? (a) 3 (b) 5 (c) 2 (d) 4
3. 3.How many factors does 83 have? (a) 3 (b) 1 (c) 2 (d) 4
4. 4.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 5 (d) 7
5. 5.How many prime numbers are there between 70 and 100? (a) 6 (b) 7 (c) 8 (d) 5
6. 6.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
7. 7.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 4 (d) 1
8. 8.How many factors does 117 have? (a) 4 (b) 6 (c) 7 (d) 5
9. 9.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5
10. 10.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 8 (d) 6
11. 11.What is the smallest prime factor of 21? (a) 3 (b) 7 (c) 2 (d) 1
12. 12.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 5 (d) 7
13. 13.How many prime numbers are there between 60 and 80? (a) 4 (b) 6 (c) 7 (d) 5
14. 14.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2 × 5⁴ (c) 2⁴ × 5 (d) 2³ × 5
15. 15.How many factors does 31 have? (a) 3 (b) 2 (c) 1 (d) 4
16. 16.How many factors does 104 have? (a) 7 (b) 6 (c) 9 (d) 8
17. 17.How many factors does 56 have? (a) 9 (b) 6 (c) 8 (d) 7
18. 18.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 1 (d) 2
19. 19.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2² × 5 (c) 2 × 5² (d) 2 × 5
20. 20.What is the smallest prime factor of 33? (a) 2 (b) 1 (c) 3 (d) 11
21. 21.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 6 (d) 9
22. 22.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
23. 23.How many prime numbers are there between 20 and 50? (a) 9 (b) 7 (c) 6 (d) 8
24. 24.What is the prime factorisation of 21? (a) 3 × 7 (b) 3 × 7² (c) 3² × 7 (d) 3³ × 7
25. 25.How many factors does 102 have? (a) 7 (b) 9 (c) 8 (d) 6
26. 26.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
27. 27.What is the smallest prime factor of 115? (a) 1 (b) 2 (c) 5 (d) 23
28. 28.How many prime numbers are there between 80 and 90? (a) 2 (b) 1 (c) 4 (d) 3
29. 29.How many prime numbers are there between 70 and 90? (a) 5 (b) 4 (c) 6 (d) 7
30. 30.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
31. 31.How many factors does 74 have? (a) 3 (b) 4 (c) 2 (d) 5
32. 32.How many factors does 72 have? (a) 11 (b) 10 (c) 13 (d) 12
33. 33.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 1 (d) 2
34. 34.How many factors does 45 have? (a) 4 (b) 7 (c) 5 (d) 6
35. 35.How many factors does 61 have? (a) 4 (b) 3 (c) 2 (d) 1
36. 36.How many factors does 30 have? (a) 9 (b) 8 (c) 7 (d) 6
37. 37.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 1 (d) 4
38. 38.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 2 (d) 7
39. 39.How many factors does 84 have? (a) 11 (b) 13 (c) 10 (d) 12
40. 40.How many prime numbers are there between 40 and 70? (a) 9 (b) 6 (c) 7 (d) 8

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