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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 157 · 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 prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 9 (d) 8
  2. 2.What is the prime factorisation of 420? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2 × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
  3. 3.How many factors does 72 have? (a) 11 (b) 10 (c) 13 (d) 12
  4. 4.What is the smallest prime factor of 299? (a) 23 (b) 13 (c) 2 (d) 1
  5. 5.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2² × 3² × 7
  6. 6.How many factors does 88 have? (a) 9 (b) 6 (c) 7 (d) 8
  7. 7.How many factors does 31 have? (a) 3 (b) 4 (c) 1 (d) 2
  8. 8.How many factors does 110 have? (a) 9 (b) 7 (c) 6 (d) 8
  9. 9.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2⁴ × 7 (d) 2³ × 7
  10. 10.What is the smallest prime factor of 21? (a) 2 (b) 3 (c) 7 (d) 1
  11. 11.How many prime numbers are there between 10 and 30? (a) 5 (b) 8 (c) 7 (d) 6
  12. 12.How many factors does 32 have? (a) 4 (b) 7 (c) 5 (d) 6
  13. 13.How many factors does 44 have? (a) 6 (b) 5 (c) 4 (d) 7
  14. 14.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2 × 5³ (c) 2² × 5 (d) 2⁴ × 5
  15. 15.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
  16. 16.What is the smallest prime factor of 377? (a) 13 (b) 1 (c) 2 (d) 29
  17. 17.How many factors does 111 have? (a) 5 (b) 3 (c) 4 (d) 2
  18. 18.How many factors does 66 have? (a) 6 (b) 7 (c) 9 (d) 8
  19. 19.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 2 (d) 3
  20. 20.What is the smallest prime factor of 403? (a) 31 (b) 13 (c) 1 (d) 2
  21. 21.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  22. 22.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 13 (d) 1
  23. 23.How many prime numbers are there between 80 and 100? (a) 2 (b) 5 (c) 3 (d) 4
  24. 24.What is the prime factorisation of 45? (a) 3 × 5 (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5²
  25. 25.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
  26. 26.What is the prime factorisation of 28? (a) 2² × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2 × 7
  27. 27.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 5 (d) 17
  28. 28.How many factors does 77 have? (a) 4 (b) 3 (c) 5 (d) 2
  29. 29.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5³
  30. 30.What is the smallest prime factor of 93? (a) 31 (b) 3 (c) 2 (d) 1
  31. 31.What is the smallest prime factor of 57? (a) 3 (b) 19 (c) 1 (d) 2
  32. 32.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2 × 3 × 5 (c) 2³ × 3 × 5 (d) 2² × 3 × 5
  33. 33.How many factors does 58 have? (a) 4 (b) 5 (c) 2 (d) 3
  34. 34.What is the smallest prime factor of 187? (a) 2 (b) 17 (c) 11 (d) 1
  35. 35.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
  36. 36.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2⁴ × 3 × 7
  37. 37.How many prime numbers are there between 30 and 40? (a) 1 (b) 2 (c) 3 (d) 4
  38. 38.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 8 (d) 10
  39. 39.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 8 (d) 9
  40. 40.What is the smallest prime factor of 95? (a) 5 (b) 19 (c) 2 (d) 1

Answer key

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

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