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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 34 · 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 90? (a) 2² × 3² × 5 (b) 2 × 3² × 5² (c) 2³ × 3² × 5 (d) 2 × 3² × 5
  2. 2.How many factors does 75 have? (a) 7 (b) 6 (c) 4 (d) 5
  3. 3.How many prime numbers are there between 20 and 30? (a) 3 (b) 1 (c) 4 (d) 2
  4. 4.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2 × 3² × 5³ (c) 2⁴ × 3² × 5 (d) 2³ × 3² × 5
  5. 5.How many prime numbers are there between 80 and 90? (a) 4 (b) 1 (c) 3 (d) 2
  6. 6.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 11 (d) 1
  7. 7.How many prime numbers are there between 10 and 30? (a) 6 (b) 8 (c) 7 (d) 5
  8. 8.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 9 (d) 6
  9. 9.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 11 (d) 2
  10. 10.How many prime numbers are there between 50 and 70? (a) 6 (b) 4 (c) 5 (d) 3
  11. 11.What is the smallest prime factor of 51? (a) 1 (b) 3 (c) 2 (d) 17
  12. 12.How many factors does 13 have? (a) 2 (b) 4 (c) 1 (d) 3
  13. 13.How many factors does 29 have? (a) 3 (b) 4 (c) 1 (d) 2
  14. 14.What is the smallest prime factor of 49? (a) 1 (b) 3 (c) 2 (d) 7
  15. 15.How many prime numbers are there between 10 and 20? (a) 6 (b) 3 (c) 5 (d) 4
  16. 16.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2 × 3² × 7³
  17. 17.How many factors does 106 have? (a) 4 (b) 3 (c) 2 (d) 5
  18. 18.How many factors does 19 have? (a) 3 (b) 4 (c) 2 (d) 1
  19. 19.How many prime numbers are there between 80 and 100? (a) 4 (b) 5 (c) 3 (d) 2
  20. 20.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 2 (d) 5
  21. 21.How many factors does 52 have? (a) 4 (b) 5 (c) 6 (d) 7
  22. 22.What is the smallest prime factor of 39? (a) 13 (b) 1 (c) 2 (d) 3
  23. 23.What is the smallest prime factor of 121? (a) 1 (b) 11 (c) 3 (d) 2
  24. 24.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2³ × 3²
  25. 25.How many prime numbers are there between 70 and 80? (a) 5 (b) 3 (c) 2 (d) 4
  26. 26.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 1 (d) 11
  27. 27.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 4 (d) 1
  28. 28.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
  29. 29.How many factors does 21 have? (a) 4 (b) 5 (c) 2 (d) 3
  30. 30.How many factors does 62 have? (a) 2 (b) 5 (c) 3 (d) 4
  31. 31.How many factors does 107 have? (a) 1 (b) 3 (c) 4 (d) 2
  32. 32.How many prime numbers are there between 40 and 50? (a) 4 (b) 2 (c) 5 (d) 3
  33. 33.How many factors does 63 have? (a) 7 (b) 6 (c) 5 (d) 4
  34. 34.What is the smallest prime factor of 161? (a) 23 (b) 7 (c) 1 (d) 2
  35. 35.How many factors does 119 have? (a) 2 (b) 4 (c) 3 (d) 5
  36. 36.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 2 (d) 13
  37. 37.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  38. 38.How many factors does 104 have? (a) 7 (b) 8 (c) 9 (d) 6
  39. 39.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁴ × 3
  40. 40.How many factors does 110 have? (a) 8 (b) 9 (c) 7 (d) 6

Answer key

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

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