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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 161 · 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 18? (a) 2² × 3² (b) 2 × 3³ (c) 2 × 3² (d) 2² × 3
  2. 2.How many factors does 70 have? (a) 8 (b) 7 (c) 6 (d) 9
  3. 3.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 2 (d) 17
  4. 4.How many factors does 69 have? (a) 3 (b) 4 (c) 5 (d) 2
  5. 5.How many prime numbers are there between 50 and 70? (a) 5 (b) 6 (c) 3 (d) 4
  6. 6.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 10 (d) 9
  7. 7.How many prime numbers are there between 40 and 50? (a) 5 (b) 3 (c) 4 (d) 2
  8. 8.What is the smallest prime factor of 91? (a) 2 (b) 13 (c) 7 (d) 1
  9. 9.How many factors does 19 have? (a) 4 (b) 2 (c) 3 (d) 1
  10. 10.What is the smallest prime factor of 77? (a) 7 (b) 1 (c) 2 (d) 11
  11. 11.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 2 (d) 1
  12. 12.What is the prime factorisation of 35? (a) 5² × 7 (b) 5 × 7² (c) 5 × 7 (d) 5³ × 7
  13. 13.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2³ × 3
  14. 14.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
  15. 15.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
  16. 16.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
  17. 17.What is the smallest prime factor of 253? (a) 23 (b) 11 (c) 1 (d) 2
  18. 18.How many factors does 23 have? (a) 4 (b) 3 (c) 2 (d) 1
  19. 19.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
  20. 20.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5
  21. 21.What is the smallest prime factor of 51? (a) 1 (b) 2 (c) 17 (d) 3
  22. 22.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 1 (d) 5
  23. 23.How many factors does 90 have? (a) 11 (b) 13 (c) 12 (d) 10
  24. 24.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  25. 25.What is the smallest prime factor of 87? (a) 3 (b) 2 (c) 1 (d) 29
  26. 26.What is the smallest prime factor of 39? (a) 2 (b) 1 (c) 13 (d) 3
  27. 27.How many factors does 57 have? (a) 5 (b) 2 (c) 3 (d) 4
  28. 28.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2³ × 3
  29. 29.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5²
  30. 30.How many factors does 24 have? (a) 7 (b) 9 (c) 6 (d) 8
  31. 31.How many factors does 43 have? (a) 1 (b) 3 (c) 2 (d) 4
  32. 32.What is the smallest prime factor of 403? (a) 13 (b) 1 (c) 31 (d) 2
  33. 33.What is the prime factorisation of 12? (a) 2² × 3 (b) 2³ × 3 (c) 2 × 3 (d) 2 × 3²
  34. 34.How many factors does 14 have? (a) 5 (b) 3 (c) 4 (d) 2
  35. 35.How many factors does 87 have? (a) 5 (b) 2 (c) 4 (d) 3
  36. 36.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2 × 5⁴ (c) 2⁵ × 5 (d) 2³ × 5
  37. 37.How many factors does 99 have? (a) 4 (b) 6 (c) 5 (d) 7
  38. 38.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  39. 39.How many factors does 32 have? (a) 7 (b) 5 (c) 6 (d) 4
  40. 40.How many factors does 60 have? (a) 10 (b) 12 (c) 11 (d) 13

Answer key

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

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