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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 177 · 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 360? (a) 2⁴ × 3² × 5 (b) 2 × 3² × 5³ (c) 2² × 3² × 5 (d) 2³ × 3² × 5
  2. 2.How many prime numbers are there between 20 and 50? (a) 6 (b) 9 (c) 7 (d) 8
  3. 3.How many factors does 41 have? (a) 2 (b) 4 (c) 3 (d) 1
  4. 4.How many prime numbers are there between 60 and 80? (a) 6 (b) 7 (c) 5 (d) 4
  5. 5.What is the smallest prime factor of 33? (a) 3 (b) 2 (c) 11 (d) 1
  6. 6.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
  7. 7.How many factors does 116 have? (a) 5 (b) 7 (c) 6 (d) 4
  8. 8.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
  9. 9.How many factors does 55 have? (a) 5 (b) 4 (c) 2 (d) 3
  10. 10.How many factors does 73 have? (a) 1 (b) 3 (c) 2 (d) 4
  11. 11.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3³ (d) 2 × 3²
  12. 12.What is the smallest prime factor of 95? (a) 2 (b) 1 (c) 19 (d) 5
  13. 13.What is the prime factorisation of 15? (a) 3³ × 5 (b) 3² × 5 (c) 3 × 5² (d) 3 × 5
  14. 14.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
  15. 15.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2⁵ × 7 (c) 2⁴ × 7 (d) 2 × 7⁴
  16. 16.What is the smallest prime factor of 51? (a) 3 (b) 2 (c) 1 (d) 17
  17. 17.How many factors does 93 have? (a) 5 (b) 2 (c) 4 (d) 3
  18. 18.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
  19. 19.What is the prime factorisation of 40? (a) 2⁴ × 5 (b) 2² × 5 (c) 2 × 5³ (d) 2³ × 5
  20. 20.How many factors does 63 have? (a) 7 (b) 6 (c) 5 (d) 4
  21. 21.How many factors does 110 have? (a) 6 (b) 9 (c) 7 (d) 8
  22. 22.How many prime numbers are there between 20 and 30? (a) 1 (b) 2 (c) 3 (d) 4
  23. 23.How many factors does 89 have? (a) 4 (b) 1 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 252? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2³ × 3² × 7 (d) 2² × 3² × 7
  25. 25.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
  26. 26.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 2 (d) 1
  27. 27.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
  28. 28.How many factors does 28 have? (a) 5 (b) 4 (c) 6 (d) 7
  29. 29.What is the smallest prime factor of 65? (a) 5 (b) 13 (c) 1 (d) 2
  30. 30.How many factors does 17 have? (a) 2 (b) 1 (c) 4 (d) 3
  31. 31.What is the smallest prime factor of 121? (a) 3 (b) 2 (c) 11 (d) 1
  32. 32.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
  33. 33.How many prime numbers are there between 70 and 80? (a) 2 (b) 4 (c) 5 (d) 3
  34. 34.How many factors does 97 have? (a) 2 (b) 3 (c) 4 (d) 1
  35. 35.What is the prime factorisation of 21? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
  36. 36.How many prime numbers are there between 50 and 60? (a) 2 (b) 4 (c) 3 (d) 1
  37. 37.How many prime numbers are there between 60 and 90? (a) 9 (b) 7 (c) 6 (d) 8
  38. 38.How many prime numbers are there between 90 and 120? (a) 6 (b) 5 (c) 8 (d) 7
  39. 39.How many factors does 44 have? (a) 7 (b) 4 (c) 5 (d) 6
  40. 40.How many factors does 88 have? (a) 8 (b) 7 (c) 6 (d) 9

Answer key

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

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