Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 90 · 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 108 have? (a) 11 (b) 12 (c) 10 (d) 13
2. 2.What is the smallest prime factor of 95? (a) 19 (b) 5 (c) 2 (d) 1
3. 3.What is the smallest prime factor of 87? (a) 1 (b) 2 (c) 3 (d) 29
4. 4.How many prime numbers are there between 40 and 50? (a) 4 (b) 3 (c) 5 (d) 2
5. 5.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 3 (d) 4
6. 6.What is the smallest prime factor of 115? (a) 1 (b) 5 (c) 2 (d) 23
7. 7.How many factors does 25 have? (a) 2 (b) 3 (c) 4 (d) 1
8. 8.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 8 (d) 6
9. 9.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2 × 7⁴ (c) 2³ × 7 (d) 2⁵ × 7
10. 10.What is the smallest prime factor of 377? (a) 29 (b) 2 (c) 1 (d) 13
11. 11.How many factors does 27 have? (a) 4 (b) 2 (c) 3 (d) 5
12. 12.How many factors does 38 have? (a) 2 (b) 3 (c) 4 (d) 5
13. 13.What is the prime factorisation of 63? (a) 3 × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3² × 7
14. 14.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2⁴ × 3 × 7
15. 15.How many factors does 77 have? (a) 2 (b) 4 (c) 5 (d) 3
16. 16.How many prime numbers are there between 70 and 80? (a) 3 (b) 2 (c) 5 (d) 4
17. 17.How many prime numbers are there between 50 and 60? (a) 4 (b) 2 (c) 3 (d) 1
18. 18.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 11 (d) 2
19. 19.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
20. 20.What is the smallest prime factor of 39? (a) 1 (b) 3 (c) 13 (d) 2
21. 21.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 6 (d) 8
22. 22.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 0 (d) 3
23. 23.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 7 (d) 1
24. 24.How many prime numbers are there between 10 and 40? (a) 9 (b) 8 (c) 7 (d) 10
25. 25.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5 × 7 (d) 5³ × 7
26. 26.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
27. 27.What is the smallest prime factor of 143? (a) 11 (b) 2 (c) 13 (d) 1
28. 28.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 4 (d) 2
29. 29.What is the smallest prime factor of 49? (a) 2 (b) 1 (c) 3 (d) 7
30. 30.What is the prime factorisation of 14? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7 (d) 2 × 7²
31. 31.How many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
32. 32.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2 × 3² (c) 2³ × 3² (d) 2² × 3²
33. 33.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5
34. 34.How many factors does 17 have? (a) 4 (b) 2 (c) 3 (d) 1
35. 35.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 6 (d) 5
36. 36.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 4 (d) 6
37. 37.What is the smallest prime factor of 161? (a) 23 (b) 2 (c) 1 (d) 7
38. 38.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2² × 3³ (c) 2⁴ × 3² (d) 2² × 3²
39. 39.What is the smallest prime factor of 69? (a) 2 (b) 1 (c) 23 (d) 3
40. 40.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2 × 3²

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