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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 176 · 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.How many factors does 67 have? (a) 2 (b) 3 (c) 4 (d) 1
  2. 2.How many factors does 119 have? (a) 3 (b) 5 (c) 2 (d) 4
  3. 3.How many factors does 30 have? (a) 7 (b) 6 (c) 9 (d) 8
  4. 4.What is the smallest prime factor of 169? (a) 13 (b) 1 (c) 2 (d) 3
  5. 5.How many prime numbers are there between 60 and 80? (a) 6 (b) 4 (c) 7 (d) 5
  6. 6.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 5 (d) 4
  7. 7.How many prime numbers are there between 50 and 70? (a) 5 (b) 4 (c) 3 (d) 6
  8. 8.How many factors does 24 have? (a) 7 (b) 6 (c) 9 (d) 8
  9. 9.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
  10. 10.How many prime numbers are there between 20 and 30? (a) 4 (b) 1 (c) 3 (d) 2
  11. 11.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2² × 3 × 5
  12. 12.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2³ × 3² × 7 (c) 2 × 3² × 7 (d) 2² × 3² × 7
  13. 13.How many factors does 91 have? (a) 3 (b) 2 (c) 5 (d) 4
  14. 14.How many prime numbers are there between 70 and 80? (a) 4 (b) 3 (c) 2 (d) 5
  15. 15.How many factors does 55 have? (a) 4 (b) 2 (c) 3 (d) 5
  16. 16.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3 × 5 × 7
  17. 17.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 2 (d) 5
  18. 18.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
  19. 19.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
  20. 20.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 9 (d) 7
  21. 21.How many factors does 76 have? (a) 4 (b) 7 (c) 6 (d) 5
  22. 22.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
  23. 23.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  24. 24.How many factors does 107 have? (a) 4 (b) 3 (c) 1 (d) 2
  25. 25.What is the prime factorisation of 45? (a) 3 × 5² (b) 3³ × 5 (c) 3 × 5 (d) 3² × 5
  26. 26.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3³ × 5 × 7 (d) 3² × 5 × 7
  27. 27.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 9 (d) 6
  28. 28.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
  29. 29.How many prime numbers are there between 40 and 60? (a) 5 (b) 7 (c) 4 (d) 6
  30. 30.How many factors does 101 have? (a) 1 (b) 2 (c) 4 (d) 3
  31. 31.What is the smallest prime factor of 65? (a) 13 (b) 1 (c) 2 (d) 5
  32. 32.What is the smallest prime factor of 403? (a) 2 (b) 1 (c) 31 (d) 13
  33. 33.What is the smallest prime factor of 121? (a) 11 (b) 1 (c) 3 (d) 2
  34. 34.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2⁴ × 3
  35. 35.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 9 (d) 8
  36. 36.How many factors does 32 have? (a) 4 (b) 5 (c) 7 (d) 6
  37. 37.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3 × 7 (c) 3 × 7² (d) 3² × 7
  38. 38.How many factors does 97 have? (a) 4 (b) 1 (c) 2 (d) 3
  39. 39.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  40. 40.How many factors does 92 have? (a) 7 (b) 5 (c) 4 (d) 6

Answer key

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

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