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Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 152 · 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 33? (a) 11 (b) 3 (c) 2 (d) 1
  2. 2.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 6 (d) 7
  3. 3.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  4. 4.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  5. 5.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2 × 3² (c) 2² × 3² (d) 2³ × 3²
  6. 6.How many prime numbers are there between 10 and 20? (a) 4 (b) 3 (c) 6 (d) 5
  7. 7.What is the smallest prime factor of 155? (a) 31 (b) 1 (c) 5 (d) 2
  8. 8.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3³ × 5 × 7
  9. 9.How many factors does 104 have? (a) 7 (b) 6 (c) 9 (d) 8
  10. 10.What is the prime factorisation of 560? (a) 2⁵ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2³ × 5 × 7
  11. 11.What is the smallest prime factor of 143? (a) 2 (b) 11 (c) 1 (d) 13
  12. 12.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
  13. 13.How many factors does 73 have? (a) 4 (b) 2 (c) 1 (d) 3
  14. 14.How many factors does 112 have? (a) 11 (b) 8 (c) 10 (d) 9
  15. 15.What is the smallest prime factor of 203? (a) 7 (b) 2 (c) 1 (d) 29
  16. 16.How many factors does 81 have? (a) 3 (b) 5 (c) 4 (d) 6
  17. 17.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2² × 7 (c) 2⁴ × 7 (d) 2³ × 7
  18. 18.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  19. 19.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2⁵ × 7
  20. 20.How many factors does 100 have? (a) 9 (b) 10 (c) 7 (d) 8
  21. 21.How many prime numbers are there between 80 and 100? (a) 3 (b) 4 (c) 2 (d) 5
  22. 22.How many factors does 80 have? (a) 9 (b) 10 (c) 11 (d) 8
  23. 23.What is the prime factorisation of 18? (a) 2² × 3 (b) 2 × 3³ (c) 2² × 3² (d) 2 × 3²
  24. 24.How many prime numbers are there between 40 and 50? (a) 2 (b) 4 (c) 5 (d) 3
  25. 25.What is the smallest prime factor of 247? (a) 2 (b) 1 (c) 19 (d) 13
  26. 26.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
  27. 27.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2² × 3 × 5
  28. 28.What is the prime factorisation of 105? (a) 3² × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7 (d) 3 × 5 × 7²
  29. 29.How many factors does 15 have? (a) 3 (b) 2 (c) 4 (d) 5
  30. 30.How many factors does 65 have? (a) 5 (b) 4 (c) 2 (d) 3
  31. 31.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
  32. 32.What is the prime factorisation of 63? (a) 3 × 7 (b) 3 × 7² (c) 3³ × 7 (d) 3² × 7
  33. 33.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 5 (d) 4
  34. 34.How many factors does 88 have? (a) 6 (b) 7 (c) 9 (d) 8
  35. 35.How many prime numbers are there between 50 and 80? (a) 9 (b) 7 (c) 6 (d) 8
  36. 36.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2⁵ × 5 (c) 2³ × 5 (d) 2⁴ × 5
  37. 37.What is the prime factorisation of 40? (a) 2² × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5³
  38. 38.How many factors does 111 have? (a) 2 (b) 5 (c) 3 (d) 4
  39. 39.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2³ × 3 × 5
  40. 40.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 6 (d) 5

Answer key

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

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