Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 67 · 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.How many factors does 62 have? (a) 5 (b) 3 (c) 2 (d) 4
2. 2.How many factors does 54 have? (a) 7 (b) 8 (c) 9 (d) 6
3. 3.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 7 (d) 3
4. 4.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 29 (d) 5
5. 5.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
6. 6.What is the smallest prime factor of 93? (a) 3 (b) 31 (c) 2 (d) 1
7. 7.How many factors does 106 have? (a) 2 (b) 3 (c) 4 (d) 5
8. 8.How many factors does 79 have? (a) 2 (b) 1 (c) 4 (d) 3
9. 9.What is the prime factorisation of 560? (a) 2³ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2 × 5 × 7⁴ (d) 2⁵ × 5 × 7
10. 10.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
11. 11.How many prime numbers are there between 60 and 90? (a) 6 (b) 9 (c) 8 (d) 7
12. 12.How many prime numbers are there between 10 and 30? (a) 5 (b) 8 (c) 7 (d) 6
13. 13.What is the smallest prime factor of 221? (a) 1 (b) 17 (c) 2 (d) 13
14. 14.How many factors does 19 have? (a) 1 (b) 2 (c) 4 (d) 3
15. 15.What is the smallest prime factor of 69? (a) 3 (b) 23 (c) 1 (d) 2
16. 16.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2 × 3³ (c) 2² × 3 (d) 2⁴ × 3
17. 17.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 4 (d) 1
18. 18.How many factors does 55 have? (a) 5 (b) 3 (c) 4 (d) 2
19. 19.What is the smallest prime factor of 203? (a) 7 (b) 29 (c) 1 (d) 2
20. 20.How many factors does 69 have? (a) 5 (b) 4 (c) 3 (d) 2
21. 21.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 5 (d) 4
22. 22.How many factors does 116 have? (a) 7 (b) 6 (c) 4 (d) 5
23. 23.What is the smallest prime factor of 115? (a) 5 (b) 1 (c) 2 (d) 23
24. 24.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7
25. 25.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2² × 3² × 7
26. 26.How many factors does 29 have? (a) 4 (b) 1 (c) 2 (d) 3
27. 27.How many prime numbers are there between 50 and 60? (a) 3 (b) 4 (c) 2 (d) 1
28. 28.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
29. 29.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 13 (d) 2
30. 30.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2² × 3⁴ (c) 2⁵ × 3² (d) 2³ × 3²
31. 31.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 11 (d) 7
32. 32.What is the prime factorisation of 15? (a) 3² × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3 × 5
33. 33.How many factors does 14 have? (a) 2 (b) 3 (c) 4 (d) 5
34. 34.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 31 (d) 5
35. 35.How many prime numbers are there between 90 and 110? (a) 4 (b) 6 (c) 7 (d) 5
36. 36.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2³ × 3 × 7
37. 37.How many factors does 49 have? (a) 2 (b) 4 (c) 3 (d) 1
38. 38.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
39. 39.How many factors does 38 have? (a) 3 (b) 2 (c) 5 (d) 4
40. 40.How many prime numbers are there between 80 and 100? (a) 4 (b) 2 (c) 3 (d) 5

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