← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 14 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2 × 3² × 5 (d) 2³ × 3² × 5
  2. 2.How many factors does 16 have? (a) 5 (b) 3 (c) 4 (d) 6
  3. 3.How many factors does 105 have? (a) 6 (b) 8 (c) 9 (d) 7
  4. 4.How many prime numbers are there between 20 and 30? (a) 4 (b) 3 (c) 2 (d) 1
  5. 5.How many factors does 104 have? (a) 9 (b) 7 (c) 6 (d) 8
  6. 6.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 23 (d) 13
  7. 7.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 6 (d) 7
  8. 8.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 7 (d) 1
  9. 9.What is the smallest prime factor of 77? (a) 11 (b) 2 (c) 7 (d) 1
  10. 10.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 6 (d) 7
  11. 11.How many factors does 37 have? (a) 3 (b) 4 (c) 1 (d) 2
  12. 12.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2³ × 3 × 7
  13. 13.What is the smallest prime factor of 33? (a) 3 (b) 11 (c) 2 (d) 1
  14. 14.How many factors does 26 have? (a) 2 (b) 3 (c) 4 (d) 5
  15. 15.What is the smallest prime factor of 51? (a) 3 (b) 2 (c) 1 (d) 17
  16. 16.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2 × 7⁴ (c) 2⁵ × 7 (d) 2³ × 7
  17. 17.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
  18. 18.How many prime numbers are there between 50 and 60? (a) 1 (b) 2 (c) 4 (d) 3
  19. 19.How many prime numbers are there between 80 and 110? (a) 6 (b) 8 (c) 7 (d) 9
  20. 20.How many factors does 14 have? (a) 2 (b) 4 (c) 5 (d) 3
  21. 21.How many factors does 72 have? (a) 10 (b) 12 (c) 11 (d) 13
  22. 22.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2² × 5 × 7
  23. 23.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 4 (d) 3
  24. 24.How many factors does 29 have? (a) 4 (b) 2 (c) 3 (d) 1
  25. 25.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
  26. 26.What is the prime factorisation of 36? (a) 2² × 3² (b) 2 × 3² (c) 2³ × 3² (d) 2² × 3³
  27. 27.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 5 (d) 6
  28. 28.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 7 (d) 9
  29. 29.How many factors does 34 have? (a) 5 (b) 4 (c) 2 (d) 3
  30. 30.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2² × 3⁴ (c) 2³ × 3² (d) 2⁴ × 3²
  31. 31.What is the prime factorisation of 21? (a) 3 × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3² × 7
  32. 32.How many factors does 32 have? (a) 7 (b) 4 (c) 6 (d) 5
  33. 33.How many factors does 68 have? (a) 6 (b) 4 (c) 7 (d) 5
  34. 34.How many factors does 86 have? (a) 4 (b) 3 (c) 2 (d) 5
  35. 35.How many prime numbers are there between 40 and 50? (a) 2 (b) 5 (c) 3 (d) 4
  36. 36.What is the smallest prime factor of 161? (a) 7 (b) 1 (c) 23 (d) 2
  37. 37.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 2 (d) 1
  38. 38.How many factors does 15 have? (a) 5 (b) 3 (c) 2 (d) 4
  39. 39.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7⁴
  40. 40.How many factors does 96 have? (a) 13 (b) 12 (c) 10 (d) 11

Answer key

  1. 2 × 3² × 5
  2. 5
  3. 8
  4. 2
  5. 8
  6. 13
  7. 5
  8. 7
  9. 7
  10. 5
  11. 2
  12. 2 × 3 × 7
  13. 3
  14. 4
  15. 3
  16. 2⁴ × 7
  17. 3
  18. 2
  19. 7
  20. 4
  21. 12
  22. 2 × 5 × 7
  23. 3
  24. 2
  25. 6
  26. 2² × 3²
  27. 4
  28. 7
  29. 4
  30. 2⁴ × 3²
  31. 3 × 7
  32. 6
  33. 6
  34. 4
  35. 3
  36. 7
  37. 5
  38. 4
  39. 2⁴ × 5 × 7
  40. 12

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