Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 189 · 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 90 and 120? (a) 6 (b) 8 (c) 7 (d) 5
2. 2.What is the smallest prime factor of 69? (a) 2 (b) 23 (c) 3 (d) 1
3. 3.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2³ × 3 × 7 (d) 2² × 3 × 7
4. 4.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 3 (d) 2
5. 5.What is the smallest prime factor of 55? (a) 11 (b) 2 (c) 5 (d) 1
6. 6.How many factors does 120 have? (a) 15 (b) 14 (c) 17 (d) 16
7. 7.What is the smallest prime factor of 161? (a) 23 (b) 1 (c) 2 (d) 7
8. 8.How many prime numbers are there between 70 and 90? (a) 6 (b) 7 (c) 5 (d) 4
9. 9.How many prime numbers are there between 50 and 80? (a) 6 (b) 9 (c) 8 (d) 7
10. 10.How many factors does 22 have? (a) 4 (b) 3 (c) 2 (d) 5
11. 11.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7⁴
12. 12.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 5 (d) 8
13. 13.How many factors does 39 have? (a) 2 (b) 4 (c) 5 (d) 3
14. 14.How many factors does 91 have? (a) 3 (b) 4 (c) 2 (d) 5
15. 15.How many prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 3 (d) 4
16. 16.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2⁴ × 3² (c) 2² × 3² (d) 2³ × 3²
17. 17.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 7 (d) 5
18. 18.What is the prime factorisation of 40? (a) 2 × 5³ (b) 2⁴ × 5 (c) 2² × 5 (d) 2³ × 5
19. 19.How many prime numbers are there between 80 and 90? (a) 3 (b) 2 (c) 4 (d) 1
20. 20.How many factors does 97 have? (a) 2 (b) 3 (c) 4 (d) 1
21. 21.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3 (c) 2² × 3² (d) 2 × 3²
22. 22.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2⁴ × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
23. 23.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 2 (d) 3
24. 24.How many prime numbers are there between 30 and 40? (a) 4 (b) 1 (c) 3 (d) 2
25. 25.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 0 (d) 2
26. 26.How many factors does 115 have? (a) 5 (b) 2 (c) 4 (d) 3
27. 27.How many factors does 110 have? (a) 7 (b) 6 (c) 8 (d) 9
28. 28.How many factors does 92 have? (a) 4 (b) 7 (c) 6 (d) 5
29. 29.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 2 (d) 1
30. 30.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3 × 7
31. 31.How many prime numbers are there between 70 and 80? (a) 3 (b) 4 (c) 5 (d) 2
32. 32.How many factors does 78 have? (a) 6 (b) 9 (c) 8 (d) 7
33. 33.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 10 (d) 9
34. 34.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 7 (d) 9
35. 35.What is the smallest prime factor of 209? (a) 11 (b) 1 (c) 19 (d) 2
36. 36.What is the smallest prime factor of 119? (a) 1 (b) 2 (c) 17 (d) 7
37. 37.What is the smallest prime factor of 87? (a) 1 (b) 3 (c) 2 (d) 29
38. 38.What is the smallest prime factor of 403? (a) 13 (b) 31 (c) 2 (d) 1
39. 39.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2³ × 5 × 7 (d) 2² × 5 × 7
40. 40.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 7 (d) 9

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