Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 214 · 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 20 and 30? (a) 2 (b) 4 (c) 3 (d) 1
2. 2.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 2 (d) 4
3. 3.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2² × 5 (d) 2³ × 5
4. 4.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 2 (d) 3
5. 5.How many factors does 115 have? (a) 5 (b) 4 (c) 3 (d) 2
6. 6.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 7 (d) 9
7. 7.What is the smallest prime factor of 217? (a) 7 (b) 2 (c) 1 (d) 31
8. 8.What is the smallest prime factor of 35? (a) 7 (b) 1 (c) 2 (d) 5
9. 9.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 5 (d) 8
10. 10.How many factors does 80 have? (a) 11 (b) 8 (c) 10 (d) 9
11. 11.How many prime numbers are there between 30 and 60? (a) 8 (b) 7 (c) 6 (d) 9
12. 12.How many factors does 23 have? (a) 2 (b) 1 (c) 3 (d) 4
13. 13.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 5 (d) 11
14. 14.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
15. 15.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 4 (d) 3
16. 16.How many factors does 69 have? (a) 3 (b) 5 (c) 2 (d) 4
17. 17.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
18. 18.How many factors does 79 have? (a) 1 (b) 4 (c) 3 (d) 2
19. 19.How many factors does 67 have? (a) 3 (b) 4 (c) 1 (d) 2
20. 20.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 2 (d) 7
21. 21.How many factors does 118 have? (a) 4 (b) 5 (c) 2 (d) 3
22. 22.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 8 (d) 10
23. 23.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
24. 24.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
25. 25.How many factors does 101 have? (a) 4 (b) 1 (c) 3 (d) 2
26. 26.How many factors does 111 have? (a) 3 (b) 5 (c) 2 (d) 4
27. 27.How many factors does 54 have? (a) 6 (b) 9 (c) 7 (d) 8
28. 28.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2 × 3²
29. 29.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
30. 30.How many factors does 52 have? (a) 4 (b) 6 (c) 5 (d) 7
31. 31.How many factors does 87 have? (a) 4 (b) 5 (c) 2 (d) 3
32. 32.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2⁴ × 3² × 7 (c) 2 × 3² × 7³ (d) 2³ × 3² × 7
33. 33.How many factors does 107 have? (a) 1 (b) 3 (c) 4 (d) 2
34. 34.How many prime numbers are there between 90 and 120? (a) 8 (b) 7 (c) 5 (d) 6
35. 35.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
36. 36.How many factors does 48 have? (a) 8 (b) 10 (c) 11 (d) 9
37. 37.What is the smallest prime factor of 95? (a) 5 (b) 19 (c) 2 (d) 1
38. 38.How many prime numbers are there between 20 and 50? (a) 6 (b) 8 (c) 9 (d) 7
39. 39.How many factors does 112 have? (a) 9 (b) 11 (c) 8 (d) 10
40. 40.How many factors does 81 have? (a) 6 (b) 3 (c) 4 (d) 5

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad