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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 51 · 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 100 have? (a) 8 (b) 7 (c) 9 (d) 10
  2. 2.What is the smallest prime factor of 221? (a) 13 (b) 17 (c) 1 (d) 2
  3. 3.What is the prime factorisation of 72? (a) 2³ × 3² (b) 2⁴ × 3² (c) 2² × 3² (d) 2² × 3³
  4. 4.How many factors does 86 have? (a) 4 (b) 3 (c) 5 (d) 2
  5. 5.How many factors does 51 have? (a) 2 (b) 3 (c) 5 (d) 4
  6. 6.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
  7. 7.How many prime numbers are there between 30 and 40? (a) 2 (b) 1 (c) 4 (d) 3
  8. 8.How many prime numbers are there between 90 and 120? (a) 7 (b) 6 (c) 5 (d) 8
  9. 9.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2⁴ × 7 (d) 2 × 7⁴
  10. 10.How many factors does 93 have? (a) 5 (b) 2 (c) 3 (d) 4
  11. 11.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 6 (d) 7
  12. 12.What is the smallest prime factor of 35? (a) 1 (b) 2 (c) 7 (d) 5
  13. 13.How many prime numbers are there between 70 and 80? (a) 3 (b) 2 (c) 5 (d) 4
  14. 14.What is the smallest prime factor of 119? (a) 2 (b) 17 (c) 1 (d) 7
  15. 15.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2 × 3² × 7
  16. 16.How many factors does 104 have? (a) 6 (b) 7 (c) 8 (d) 9
  17. 17.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
  18. 18.What is the smallest prime factor of 377? (a) 13 (b) 2 (c) 1 (d) 29
  19. 19.How many factors does 111 have? (a) 2 (b) 4 (c) 5 (d) 3
  20. 20.How many factors does 17 have? (a) 3 (b) 2 (c) 4 (d) 1
  21. 21.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7³ (d) 2³ × 5 × 7
  22. 22.How many factors does 103 have? (a) 4 (b) 1 (c) 2 (d) 3
  23. 23.How many factors does 80 have? (a) 10 (b) 8 (c) 9 (d) 11
  24. 24.How many factors does 15 have? (a) 3 (b) 2 (c) 4 (d) 5
  25. 25.How many factors does 46 have? (a) 4 (b) 5 (c) 3 (d) 2
  26. 26.What is the prime factorisation of 20? (a) 2 × 5² (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5
  27. 27.What is the smallest prime factor of 217? (a) 7 (b) 2 (c) 31 (d) 1
  28. 28.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 0 (d) 3
  29. 29.How many factors does 94 have? (a) 5 (b) 3 (c) 4 (d) 2
  30. 30.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 1 (d) 5
  31. 31.How many factors does 33 have? (a) 3 (b) 5 (c) 2 (d) 4
  32. 32.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
  33. 33.How many prime numbers are there between 20 and 50? (a) 6 (b) 7 (c) 8 (d) 9
  34. 34.How many factors does 96 have? (a) 11 (b) 10 (c) 13 (d) 12
  35. 35.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  36. 36.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2² × 7 (d) 2³ × 7
  37. 37.What is the smallest prime factor of 169? (a) 13 (b) 1 (c) 2 (d) 3
  38. 38.What is the smallest prime factor of 115? (a) 23 (b) 2 (c) 1 (d) 5
  39. 39.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 7 (d) 8
  40. 40.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5² (d) 2 × 3² × 5

Answer key

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

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