Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 74 · 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 60 and 90? (a) 6 (b) 9 (c) 8 (d) 7
2. 2.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
3. 3.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
4. 4.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
5. 5.How many factors does 63 have? (a) 6 (b) 5 (c) 7 (d) 4
6. 6.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 7 (d) 6
7. 7.What is the prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2² × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2³ × 5 × 7
8. 8.What is the smallest prime factor of 119? (a) 1 (b) 17 (c) 7 (d) 2
9. 9.What is the prime factorisation of 18? (a) 2² × 3² (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3
10. 10.What is the prime factorisation of 168? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7³
11. 11.How many factors does 93 have? (a) 3 (b) 2 (c) 4 (d) 5
12. 12.What is the smallest prime factor of 93? (a) 1 (b) 3 (c) 31 (d) 2
13. 13.How many factors does 50 have? (a) 4 (b) 5 (c) 6 (d) 7
14. 14.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 6 (d) 5
15. 15.How many prime numbers are there between 70 and 80? (a) 4 (b) 5 (c) 3 (d) 2
16. 16.How many prime numbers are there between 50 and 80? (a) 9 (b) 8 (c) 7 (d) 6
17. 17.How many prime numbers are there between 60 and 70? (a) 2 (b) 3 (c) 1 (d) 4
18. 18.What is the smallest prime factor of 95? (a) 2 (b) 5 (c) 19 (d) 1
19. 19.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 7 (d) 1
20. 20.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5³ (d) 2³ × 3 × 5
21. 21.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2³ × 3 × 7
22. 22.How many factors does 14 have? (a) 3 (b) 4 (c) 2 (d) 5
23. 23.How many factors does 120 have? (a) 16 (b) 17 (c) 15 (d) 14
24. 24.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁵ × 5 (d) 2⁴ × 5
25. 25.How many factors does 15 have? (a) 2 (b) 3 (c) 4 (d) 5
26. 26.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 13 (d) 17
27. 27.How many factors does 67 have? (a) 3 (b) 4 (c) 1 (d) 2
28. 28.How many factors does 51 have? (a) 4 (b) 5 (c) 2 (d) 3
29. 29.How many factors does 61 have? (a) 3 (b) 1 (c) 4 (d) 2
30. 30.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 6 (d) 5
31. 31.What is the smallest prime factor of 209? (a) 19 (b) 11 (c) 2 (d) 1
32. 32.How many factors does 38 have? (a) 5 (b) 3 (c) 2 (d) 4
33. 33.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁵ × 7 (d) 2⁴ × 7
34. 34.How many factors does 17 have? (a) 2 (b) 4 (c) 3 (d) 1
35. 35.What is the smallest prime factor of 55? (a) 5 (b) 11 (c) 1 (d) 2
36. 36.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
37. 37.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 5 (d) 7
38. 38.What is the smallest prime factor of 299? (a) 13 (b) 2 (c) 1 (d) 23
39. 39.What is the smallest prime factor of 87? (a) 3 (b) 29 (c) 2 (d) 1
40. 40.How many factors does 58 have? (a) 2 (b) 4 (c) 5 (d) 3

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