Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 1 · 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 prime factorisation of 280? (a) 2 × 5 × 7³ (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
2. 2.How many prime numbers are there between 80 and 110? (a) 7 (b) 6 (c) 9 (d) 8
3. 3.How many prime numbers are there between 40 and 70? (a) 7 (b) 8 (c) 6 (d) 9
4. 4.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
5. 5.What is the smallest prime factor of 155? (a) 31 (b) 2 (c) 1 (d) 5
6. 6.What is the prime factorisation of 30? (a) 2 × 3 × 5 (b) 2 × 3 × 5² (c) 2² × 3 × 5 (d) 2³ × 3 × 5
7. 7.How many factors does 39 have? (a) 4 (b) 5 (c) 3 (d) 2
8. 8.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
9. 9.What is the prime factorisation of 18? (a) 2² × 3² (b) 2² × 3 (c) 2 × 3³ (d) 2 × 3²
10. 10.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 11 (d) 2
11. 11.How many factors does 35 have? (a) 4 (b) 3 (c) 5 (d) 2
12. 12.What is the prime factorisation of 315? (a) 3 × 5 × 7 (b) 3 × 5 × 7² (c) 3² × 5 × 7 (d) 3³ × 5 × 7
13. 13.How many prime numbers are there between 20 and 30? (a) 2 (b) 1 (c) 4 (d) 3
14. 14.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 2 (d) 11
15. 15.What is the smallest prime factor of 69? (a) 1 (b) 2 (c) 23 (d) 3
16. 16.What is the smallest prime factor of 55? (a) 1 (b) 5 (c) 11 (d) 2
17. 17.How many factors does 16 have? (a) 5 (b) 3 (c) 4 (d) 6
18. 18.What is the smallest prime factor of 85? (a) 2 (b) 17 (c) 5 (d) 1
19. 19.What is the prime factorisation of 180? (a) 2³ × 3² × 5 (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2 × 3² × 5²
20. 20.How many factors does 67 have? (a) 1 (b) 3 (c) 2 (d) 4
21. 21.How many factors does 86 have? (a) 2 (b) 3 (c) 5 (d) 4
22. 22.What is the smallest prime factor of 33? (a) 1 (b) 11 (c) 2 (d) 3
23. 23.What is the smallest prime factor of 77? (a) 2 (b) 7 (c) 1 (d) 11
24. 24.How many prime numbers are there between 70 and 100? (a) 7 (b) 5 (c) 8 (d) 6
25. 25.What is the smallest prime factor of 145? (a) 29 (b) 2 (c) 1 (d) 5
26. 26.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 7 (d) 6
27. 27.How many prime numbers are there between 90 and 120? (a) 6 (b) 7 (c) 8 (d) 5
28. 28.How many factors does 60 have? (a) 12 (b) 13 (c) 11 (d) 10
29. 29.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 2 (d) 3
30. 30.How many prime numbers are there between 10 and 30? (a) 5 (b) 8 (c) 7 (d) 6
31. 31.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 7 (d) 4
32. 32.What is the prime factorisation of 35? (a) 5 × 7 (b) 5² × 7 (c) 5³ × 7 (d) 5 × 7²
33. 33.How many factors does 110 have? (a) 7 (b) 9 (c) 6 (d) 8
34. 34.How many prime numbers are there between 10 and 20? (a) 3 (b) 6 (c) 4 (d) 5
35. 35.How many factors does 31 have? (a) 1 (b) 3 (c) 4 (d) 2
36. 36.How many prime numbers are there between 80 and 90? (a) 1 (b) 2 (c) 4 (d) 3
37. 37.How many factors does 21 have? (a) 4 (b) 2 (c) 3 (d) 5
38. 38.How many factors does 17 have? (a) 1 (b) 4 (c) 2 (d) 3
39. 39.What is the prime factorisation of 72? (a) 2² × 3³ (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3²
40. 40.How many prime numbers are there between 50 and 70? (a) 3 (b) 5 (c) 6 (d) 4

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