← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 10 · 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 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2 × 3² × 7
  2. 2.How many factors does 68 have? (a) 7 (b) 5 (c) 4 (d) 6
  3. 3.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
  4. 4.How many factors does 83 have? (a) 3 (b) 4 (c) 1 (d) 2
  5. 5.How many factors does 31 have? (a) 4 (b) 1 (c) 3 (d) 2
  6. 6.How many prime numbers are there between 60 and 80? (a) 4 (b) 5 (c) 7 (d) 6
  7. 7.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 5 (d) 3
  8. 8.What is the prime factorisation of 48? (a) 2⁴ × 3 (b) 2³ × 3 (c) 2 × 3⁴ (d) 2⁵ × 3
  9. 9.How many factors does 74 have? (a) 3 (b) 5 (c) 4 (d) 2
  10. 10.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
  11. 11.What is the prime factorisation of 80? (a) 2³ × 5 (b) 2⁵ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
  12. 12.How many prime numbers are there between 80 and 90? (a) 4 (b) 1 (c) 3 (d) 2
  13. 13.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
  14. 14.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 2 (d) 7
  15. 15.What is the smallest prime factor of 121? (a) 2 (b) 1 (c) 3 (d) 11
  16. 16.How many factors does 91 have? (a) 4 (b) 3 (c) 5 (d) 2
  17. 17.How many factors does 79 have? (a) 1 (b) 2 (c) 4 (d) 3
  18. 18.How many factors does 111 have? (a) 4 (b) 5 (c) 3 (d) 2
  19. 19.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
  20. 20.How many factors does 108 have? (a) 10 (b) 11 (c) 13 (d) 12
  21. 21.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 2 (d) 3
  22. 22.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
  23. 23.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2⁵ × 3²
  24. 24.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6
  25. 25.What is the smallest prime factor of 253? (a) 11 (b) 2 (c) 1 (d) 23
  26. 26.How many factors does 98 have? (a) 7 (b) 4 (c) 5 (d) 6
  27. 27.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 3 (d) 2
  28. 28.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
  29. 29.How many factors does 86 have? (a) 5 (b) 2 (c) 3 (d) 4
  30. 30.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2 × 3 × 7⁴
  31. 31.What is the smallest prime factor of 119? (a) 1 (b) 7 (c) 17 (d) 2
  32. 32.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
  33. 33.How many prime numbers are there between 30 and 60? (a) 6 (b) 9 (c) 7 (d) 8
  34. 34.How many prime numbers are there between 90 and 100? (a) 2 (b) 3 (c) 1 (d) 0
  35. 35.What is the smallest prime factor of 169? (a) 1 (b) 2 (c) 3 (d) 13
  36. 36.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3³ × 5 (d) 3 × 5
  37. 37.What is the smallest prime factor of 403? (a) 2 (b) 31 (c) 13 (d) 1
  38. 38.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2 × 3² × 7³ (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
  39. 39.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2³ × 7 (d) 2⁴ × 7
  40. 40.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²

Answer key

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

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