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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 6 · 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 smallest prime factor of 115? (a) 1 (b) 2 (c) 5 (d) 23
  2. 2.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3² (d) 2² × 3³
  3. 3.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 1 (d) 2
  4. 4.How many factors does 29 have? (a) 2 (b) 3 (c) 1 (d) 4
  5. 5.What is the smallest prime factor of 35? (a) 1 (b) 7 (c) 5 (d) 2
  6. 6.How many prime numbers are there between 80 and 110? (a) 8 (b) 6 (c) 9 (d) 7
  7. 7.What is the smallest prime factor of 55? (a) 2 (b) 11 (c) 5 (d) 1
  8. 8.How many factors does 69 have? (a) 3 (b) 5 (c) 2 (d) 4
  9. 9.How many factors does 104 have? (a) 7 (b) 9 (c) 8 (d) 6
  10. 10.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5 × 7 (d) 5² × 7
  11. 11.How many prime numbers are there between 90 and 110? (a) 5 (b) 6 (c) 4 (d) 7
  12. 12.What is the smallest prime factor of 247? (a) 13 (b) 2 (c) 1 (d) 19
  13. 13.How many factors does 53 have? (a) 1 (b) 4 (c) 3 (d) 2
  14. 14.How many factors does 73 have? (a) 2 (b) 3 (c) 1 (d) 4
  15. 15.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7
  16. 16.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 9 (d) 7
  17. 17.How many factors does 106 have? (a) 2 (b) 4 (c) 5 (d) 3
  18. 18.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2⁴ × 3² (c) 2² × 3⁴ (d) 2³ × 3²
  19. 19.How many prime numbers are there between 20 and 40? (a) 4 (b) 3 (c) 6 (d) 5
  20. 20.How many prime numbers are there between 90 and 100? (a) 2 (b) 0 (c) 3 (d) 1
  21. 21.What is the prime factorisation of 72? (a) 2² × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3³
  22. 22.How many prime numbers are there between 50 and 80? (a) 9 (b) 8 (c) 7 (d) 6
  23. 23.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 3 (d) 1
  24. 24.How many factors does 56 have? (a) 7 (b) 6 (c) 8 (d) 9
  25. 25.What is the smallest prime factor of 57? (a) 2 (b) 3 (c) 19 (d) 1
  26. 26.How many prime numbers are there between 60 and 70? (a) 3 (b) 4 (c) 2 (d) 1
  27. 27.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
  28. 28.What is the prime factorisation of 120? (a) 2 × 3 × 5³ (b) 2⁴ × 3 × 5 (c) 2² × 3 × 5 (d) 2³ × 3 × 5
  29. 29.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 7 (d) 6
  30. 30.How many factors does 64 have? (a) 8 (b) 6 (c) 7 (d) 5
  31. 31.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
  32. 32.How many factors does 19 have? (a) 3 (b) 4 (c) 2 (d) 1
  33. 33.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7³ (c) 2² × 5 × 7 (d) 2³ × 5 × 7
  34. 34.How many factors does 71 have? (a) 3 (b) 1 (c) 2 (d) 4
  35. 35.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 7 (d) 8
  36. 36.How many factors does 36 have? (a) 8 (b) 9 (c) 7 (d) 10
  37. 37.How many factors does 44 have? (a) 5 (b) 7 (c) 6 (d) 4
  38. 38.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2 × 3 × 5
  39. 39.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  40. 40.How many factors does 26 have? (a) 5 (b) 2 (c) 3 (d) 4

Answer key

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

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