Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 73 · 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 prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
2. 2.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 7 (d) 2
3. 3.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3 × 5² (c) 3 × 5 (d) 3² × 5
4. 4.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
5. 5.How many factors does 13 have? (a) 3 (b) 2 (c) 4 (d) 1
6. 6.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 5 (d) 3
7. 7.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 6 (d) 8
8. 8.How many prime numbers are there between 60 and 90? (a) 7 (b) 6 (c) 8 (d) 9
9. 9.What is the smallest prime factor of 221? (a) 13 (b) 1 (c) 17 (d) 2
10. 10.How many factors does 16 have? (a) 3 (b) 5 (c) 4 (d) 6
11. 11.How many factors does 107 have? (a) 4 (b) 1 (c) 2 (d) 3
12. 12.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
13. 13.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
14. 14.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 5 (d) 7
15. 15.What is the smallest prime factor of 247? (a) 2 (b) 13 (c) 1 (d) 19
16. 16.How many factors does 18 have? (a) 7 (b) 4 (c) 5 (d) 6
17. 17.What is the smallest prime factor of 143? (a) 11 (b) 2 (c) 1 (d) 13
18. 18.How many factors does 110 have? (a) 8 (b) 7 (c) 6 (d) 9
19. 19.How many factors does 57 have? (a) 3 (b) 4 (c) 2 (d) 5
20. 20.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
21. 21.What is the smallest prime factor of 133? (a) 1 (b) 2 (c) 19 (d) 7
22. 22.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2³ × 3² (d) 2⁴ × 3²
23. 23.How many factors does 34 have? (a) 4 (b) 3 (c) 5 (d) 2
24. 24.How many factors does 21 have? (a) 3 (b) 5 (c) 2 (d) 4
25. 25.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 1 (d) 3
26. 26.How many prime numbers are there between 70 and 80? (a) 2 (b) 4 (c) 5 (d) 3
27. 27.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3³ (c) 2² × 3² (d) 2 × 3²
28. 28.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2³ × 3 × 7
29. 29.What is the smallest prime factor of 93? (a) 3 (b) 31 (c) 2 (d) 1
30. 30.How many factors does 29 have? (a) 2 (b) 3 (c) 4 (d) 1
31. 31.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7² (c) 2² × 7 (d) 2 × 7
32. 32.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 17 (d) 1
33. 33.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
34. 34.What is the smallest prime factor of 57? (a) 2 (b) 19 (c) 3 (d) 1
35. 35.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 8 (d) 6
36. 36.What is the smallest prime factor of 341? (a) 11 (b) 1 (c) 31 (d) 2
37. 37.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
38. 38.How many factors does 50 have? (a) 6 (b) 7 (c) 4 (d) 5
39. 39.How many factors does 56 have? (a) 9 (b) 8 (c) 6 (d) 7
40. 40.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 7 (d) 8

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