Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 35 · 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 53 have? (a) 1 (b) 2 (c) 3 (d) 4
2. 2.How many factors does 21 have? (a) 3 (b) 5 (c) 2 (d) 4
3. 3.What is the smallest prime factor of 341? (a) 31 (b) 11 (c) 2 (d) 1
4. 4.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 4 (d) 3
5. 5.How many prime numbers are there between 60 and 80? (a) 5 (b) 4 (c) 7 (d) 6
6. 6.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
7. 7.What is the smallest prime factor of 145? (a) 5 (b) 2 (c) 1 (d) 29
8. 8.What is the smallest prime factor of 49? (a) 2 (b) 7 (c) 3 (d) 1
9. 9.How many prime numbers are there between 30 and 60? (a) 6 (b) 7 (c) 9 (d) 8
10. 10.How many prime numbers are there between 60 and 90? (a) 8 (b) 6 (c) 7 (d) 9
11. 11.What is the smallest prime factor of 143? (a) 1 (b) 13 (c) 2 (d) 11
12. 12.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
13. 13.How many prime numbers are there between 50 and 80? (a) 9 (b) 8 (c) 7 (d) 6
14. 14.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2³ × 3² (d) 2⁴ × 3²
15. 15.How many prime numbers are there between 40 and 50? (a) 2 (b) 3 (c) 4 (d) 5
16. 16.What is the smallest prime factor of 133? (a) 2 (b) 19 (c) 7 (d) 1
17. 17.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
18. 18.What is the smallest prime factor of 21? (a) 2 (b) 7 (c) 3 (d) 1
19. 19.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3² (d) 2 × 3
20. 20.How many factors does 37 have? (a) 2 (b) 3 (c) 1 (d) 4
21. 21.What is the prime factorisation of 20? (a) 2² × 5 (b) 2³ × 5 (c) 2 × 5² (d) 2 × 5
22. 22.How many prime numbers are there between 20 and 40? (a) 4 (b) 6 (c) 3 (d) 5
23. 23.What is the prime factorisation of 63? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
24. 24.What is the smallest prime factor of 203? (a) 29 (b) 2 (c) 1 (d) 7
25. 25.What is the smallest prime factor of 39? (a) 13 (b) 2 (c) 3 (d) 1
26. 26.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 6 (d) 4
27. 27.What is the smallest prime factor of 87? (a) 3 (b) 1 (c) 29 (d) 2
28. 28.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
29. 29.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
30. 30.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 9 (d) 6
31. 31.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 4 (d) 6
32. 32.How many factors does 43 have? (a) 3 (b) 4 (c) 1 (d) 2
33. 33.How many prime numbers are there between 80 and 110? (a) 7 (b) 8 (c) 9 (d) 6
34. 34.What is the prime factorisation of 35? (a) 5 × 7² (b) 5 × 7 (c) 5³ × 7 (d) 5² × 7
35. 35.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
36. 36.How many factors does 48 have? (a) 8 (b) 9 (c) 11 (d) 10
37. 37.How many factors does 60 have? (a) 12 (b) 11 (c) 10 (d) 13
38. 38.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5³
39. 39.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 1 (d) 5
40. 40.How many prime numbers are there between 10 and 30? (a) 8 (b) 6 (c) 7 (d) 5

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