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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 204 · 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 143? (a) 1 (b) 11 (c) 2 (d) 13
  2. 2.What is the smallest prime factor of 115? (a) 2 (b) 5 (c) 23 (d) 1
  3. 3.How many prime numbers are there between 40 and 70? (a) 6 (b) 7 (c) 8 (d) 9
  4. 4.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
  5. 5.What is the prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
  6. 6.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
  7. 7.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 7 (d) 13
  8. 8.What is the smallest prime factor of 121? (a) 1 (b) 2 (c) 11 (d) 3
  9. 9.How many factors does 48 have? (a) 11 (b) 10 (c) 8 (d) 9
  10. 10.How many prime numbers are there between 40 and 50? (a) 3 (b) 4 (c) 2 (d) 5
  11. 11.What is the smallest prime factor of 161? (a) 1 (b) 2 (c) 23 (d) 7
  12. 12.How many prime numbers are there between 60 and 90? (a) 6 (b) 7 (c) 9 (d) 8
  13. 13.What is the smallest prime factor of 33? (a) 1 (b) 3 (c) 2 (d) 11
  14. 14.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 6 (d) 7
  15. 15.What is the smallest prime factor of 35? (a) 2 (b) 1 (c) 7 (d) 5
  16. 16.What is the smallest prime factor of 187? (a) 17 (b) 11 (c) 1 (d) 2
  17. 17.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 6 (d) 7
  18. 18.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  19. 19.How many factors does 112 have? (a) 9 (b) 8 (c) 10 (d) 11
  20. 20.How many prime numbers are there between 70 and 90? (a) 7 (b) 5 (c) 6 (d) 4
  21. 21.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 2 (d) 13
  22. 22.How many factors does 16 have? (a) 3 (b) 5 (c) 6 (d) 4
  23. 23.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5² × 7 (d) 5 × 7²
  24. 24.What is the smallest prime factor of 21? (a) 7 (b) 2 (c) 1 (d) 3
  25. 25.How many factors does 67 have? (a) 3 (b) 1 (c) 4 (d) 2
  26. 26.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7 (d) 2 × 7²
  27. 27.How many factors does 80 have? (a) 9 (b) 11 (c) 10 (d) 8
  28. 28.How many factors does 69 have? (a) 2 (b) 3 (c) 4 (d) 5
  29. 29.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 1 (d) 2
  30. 30.How many factors does 87 have? (a) 5 (b) 3 (c) 2 (d) 4
  31. 31.What is the smallest prime factor of 209? (a) 19 (b) 11 (c) 1 (d) 2
  32. 32.How many factors does 24 have? (a) 6 (b) 8 (c) 7 (d) 9
  33. 33.How many factors does 36 have? (a) 8 (b) 9 (c) 10 (d) 7
  34. 34.What is the smallest prime factor of 403? (a) 2 (b) 31 (c) 1 (d) 13
  35. 35.What is the smallest prime factor of 155? (a) 1 (b) 5 (c) 2 (d) 31
  36. 36.What is the smallest prime factor of 247? (a) 19 (b) 13 (c) 1 (d) 2
  37. 37.What is the smallest prime factor of 69? (a) 2 (b) 3 (c) 23 (d) 1
  38. 38.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2 × 5⁴ (d) 2⁴ × 5
  39. 39.How many factors does 117 have? (a) 7 (b) 5 (c) 6 (d) 4
  40. 40.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5

Answer key

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

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