← Primes and divisors lesson New set →

Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 22 · 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.How many prime numbers are there between 80 and 90? (a) 4 (b) 3 (c) 2 (d) 1
  2. 2.What is the smallest prime factor of 403? (a) 31 (b) 2 (c) 1 (d) 13
  3. 3.How many factors does 84 have? (a) 12 (b) 13 (c) 11 (d) 10
  4. 4.What is the smallest prime factor of 93? (a) 3 (b) 1 (c) 2 (d) 31
  5. 5.What is the smallest prime factor of 319? (a) 29 (b) 11 (c) 1 (d) 2
  6. 6.How many factors does 35 have? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.What is the smallest prime factor of 87? (a) 29 (b) 2 (c) 1 (d) 3
  8. 8.How many factors does 88 have? (a) 7 (b) 9 (c) 6 (d) 8
  9. 9.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
  10. 10.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 3 (d) 0
  11. 11.How many prime numbers are there between 60 and 80? (a) 4 (b) 6 (c) 7 (d) 5
  12. 12.How many prime numbers are there between 30 and 40? (a) 3 (b) 1 (c) 2 (d) 4
  13. 13.What is the prime factorisation of 72? (a) 2² × 3² (b) 2² × 3³ (c) 2⁴ × 3² (d) 2³ × 3²
  14. 14.What is the smallest prime factor of 161? (a) 2 (b) 1 (c) 23 (d) 7
  15. 15.What is the prime factorisation of 112? (a) 2³ × 7 (b) 2 × 7⁴ (c) 2⁴ × 7 (d) 2⁵ × 7
  16. 16.How many prime numbers are there between 80 and 110? (a) 8 (b) 9 (c) 6 (d) 7
  17. 17.What is the smallest prime factor of 209? (a) 19 (b) 1 (c) 11 (d) 2
  18. 18.How many factors does 93 have? (a) 2 (b) 5 (c) 3 (d) 4
  19. 19.How many factors does 67 have? (a) 4 (b) 3 (c) 2 (d) 1
  20. 20.What is the smallest prime factor of 91? (a) 13 (b) 7 (c) 1 (d) 2
  21. 21.How many factors does 28 have? (a) 4 (b) 5 (c) 6 (d) 7
  22. 22.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2 × 3 × 5⁴
  23. 23.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
  24. 24.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 2 (d) 29
  25. 25.How many factors does 69 have? (a) 4 (b) 3 (c) 5 (d) 2
  26. 26.How many factors does 47 have? (a) 2 (b) 3 (c) 4 (d) 1
  27. 27.How many prime numbers are there between 30 and 50? (a) 4 (b) 5 (c) 7 (d) 6
  28. 28.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁵ × 3 (d) 2⁴ × 3
  29. 29.What is the prime factorisation of 42? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
  30. 30.How many factors does 26 have? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.How many factors does 119 have? (a) 4 (b) 3 (c) 2 (d) 5
  32. 32.How many prime numbers are there between 10 and 40? (a) 7 (b) 10 (c) 9 (d) 8
  33. 33.How many factors does 52 have? (a) 5 (b) 7 (c) 4 (d) 6
  34. 34.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2⁴ × 3² × 5 (d) 2³ × 3² × 5
  35. 35.How many prime numbers are there between 70 and 90? (a) 5 (b) 6 (c) 4 (d) 7
  36. 36.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7² (d) 3 × 7
  37. 37.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2 × 7³ (c) 2² × 7 (d) 2³ × 7
  38. 38.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
  39. 39.What is the smallest prime factor of 247? (a) 2 (b) 1 (c) 19 (d) 13
  40. 40.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4

Answer key

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

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