← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 145 · 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 57? (a) 1 (b) 19 (c) 2 (d) 3
  2. 2.What is the smallest prime factor of 169? (a) 3 (b) 13 (c) 2 (d) 1
  3. 3.How many factors does 45 have? (a) 7 (b) 6 (c) 5 (d) 4
  4. 4.What is the smallest prime factor of 187? (a) 11 (b) 17 (c) 2 (d) 1
  5. 5.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
  6. 6.What is the prime factorisation of 140? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  7. 7.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3 × 7
  8. 8.How many prime numbers are there between 40 and 70? (a) 8 (b) 6 (c) 7 (d) 9
  9. 9.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  10. 10.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
  11. 11.What is the smallest prime factor of 403? (a) 1 (b) 13 (c) 2 (d) 31
  12. 12.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 10 (d) 8
  13. 13.How many prime numbers are there between 90 and 110? (a) 6 (b) 7 (c) 4 (d) 5
  14. 14.How many factors does 60 have? (a) 13 (b) 10 (c) 12 (d) 11
  15. 15.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
  16. 16.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2⁵ × 7
  17. 17.How many factors does 52 have? (a) 4 (b) 6 (c) 5 (d) 7
  18. 18.How many factors does 32 have? (a) 6 (b) 5 (c) 4 (d) 7
  19. 19.How many factors does 102 have? (a) 6 (b) 9 (c) 7 (d) 8
  20. 20.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
  21. 21.What is the smallest prime factor of 85? (a) 2 (b) 1 (c) 5 (d) 17
  22. 22.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
  23. 23.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 11 (d) 1
  24. 24.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 3 (d) 0
  25. 25.How many factors does 17 have? (a) 4 (b) 2 (c) 3 (d) 1
  26. 26.How many factors does 116 have? (a) 5 (b) 7 (c) 4 (d) 6
  27. 27.How many factors does 87 have? (a) 2 (b) 3 (c) 5 (d) 4
  28. 28.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2³ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2⁴ × 5 × 7
  29. 29.How many factors does 23 have? (a) 4 (b) 3 (c) 2 (d) 1
  30. 30.What is the smallest prime factor of 95? (a) 2 (b) 19 (c) 1 (d) 5
  31. 31.How many factors does 28 have? (a) 6 (b) 7 (c) 5 (d) 4
  32. 32.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 7 (d) 13
  33. 33.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
  34. 34.What is the smallest prime factor of 221? (a) 1 (b) 13 (c) 2 (d) 17
  35. 35.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
  36. 36.What is the smallest prime factor of 33? (a) 11 (b) 1 (c) 2 (d) 3
  37. 37.How many factors does 30 have? (a) 6 (b) 8 (c) 7 (d) 9
  38. 38.How many factors does 82 have? (a) 4 (b) 3 (c) 2 (d) 5
  39. 39.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
  40. 40.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2³ × 3² × 7

Answer key

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

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad