Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 159 · 40 questions

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.

1. 1.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
2. 2.How many factors does 113 have? (a) 4 (b) 3 (c) 1 (d) 2
3. 3.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 4 (d) 7
4. 4.What is the smallest prime factor of 77? (a) 11 (b) 7 (c) 2 (d) 1
5. 5.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 2 (d) 3
6. 6.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁴ × 3 × 7 (c) 2⁵ × 3 × 7 (d) 2 × 3 × 7⁴
7. 7.How many factors does 50 have? (a) 4 (b) 6 (c) 7 (d) 5
8. 8.What is the prime factorisation of 14? (a) 2 × 7 (b) 2² × 7 (c) 2 × 7² (d) 2³ × 7
9. 9.What is the smallest prime factor of 51? (a) 1 (b) 17 (c) 2 (d) 3
10. 10.What is the prime factorisation of 20? (a) 2³ × 5 (b) 2 × 5 (c) 2 × 5² (d) 2² × 5
11. 11.How many factors does 105 have? (a) 7 (b) 9 (c) 8 (d) 6
12. 12.How many prime numbers are there between 80 and 110? (a) 9 (b) 8 (c) 6 (d) 7
13. 13.How many factors does 14 have? (a) 2 (b) 4 (c) 3 (d) 5
14. 14.How many prime numbers are there between 70 and 90? (a) 6 (b) 5 (c) 7 (d) 4
15. 15.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 7 (d) 5
16. 16.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
17. 17.How many prime numbers are there between 10 and 30? (a) 5 (b) 8 (c) 6 (d) 7
18. 18.How many factors does 58 have? (a) 3 (b) 5 (c) 4 (d) 2
19. 19.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 6 (d) 5
20. 20.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 8 (d) 7
21. 21.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
22. 22.How many prime numbers are there between 60 and 80? (a) 7 (b) 5 (c) 4 (d) 6
23. 23.What is the smallest prime factor of 21? (a) 3 (b) 2 (c) 1 (d) 7
24. 24.What is the smallest prime factor of 49? (a) 3 (b) 7 (c) 1 (d) 2
25. 25.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 5 (d) 3
26. 26.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 7 (d) 1
27. 27.How many factors does 82 have? (a) 5 (b) 3 (c) 4 (d) 2
28. 28.How many factors does 80 have? (a) 9 (b) 10 (c) 11 (d) 8
29. 29.How many factors does 22 have? (a) 5 (b) 3 (c) 2 (d) 4
30. 30.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5
31. 31.How many factors does 24 have? (a) 6 (b) 7 (c) 9 (d) 8
32. 32.What is the smallest prime factor of 39? (a) 2 (b) 1 (c) 13 (d) 3
33. 33.What is the smallest prime factor of 253? (a) 2 (b) 23 (c) 11 (d) 1
34. 34.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 1 (d) 4
35. 35.How many factors does 89 have? (a) 3 (b) 2 (c) 4 (d) 1
36. 36.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁵ × 7 (c) 2³ × 7 (d) 2⁴ × 7
37. 37.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2³ × 3² × 5
38. 38.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 1 (d) 11
39. 39.What is the prime factorisation of 360? (a) 2⁴ × 3² × 5 (b) 2³ × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5³
40. 40.How many factors does 79 have? (a) 1 (b) 4 (c) 2 (d) 3

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