Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 212 · 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 55? (a) 5 (b) 11 (c) 2 (d) 1
2. 2.How many factors does 92 have? (a) 5 (b) 4 (c) 6 (d) 7
3. 3.What is the smallest prime factor of 403? (a) 31 (b) 1 (c) 13 (d) 2
4. 4.How many prime numbers are there between 30 and 60? (a) 7 (b) 8 (c) 6 (d) 9
5. 5.What is the prime factorisation of 18? (a) 2 × 3² (b) 2 × 3³ (c) 2² × 3 (d) 2² × 3²
6. 6.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2 × 7⁴ (c) 2⁵ × 7 (d) 2³ × 7
7. 7.What is the smallest prime factor of 169? (a) 1 (b) 2 (c) 3 (d) 13
8. 8.What is the prime factorisation of 42? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2 × 3 × 7 (d) 2² × 3 × 7
9. 9.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5² (d) 2 × 3 × 5
10. 10.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 17 (d) 13
11. 11.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
12. 12.What is the prime factorisation of 35? (a) 5 × 7 (b) 5³ × 7 (c) 5 × 7² (d) 5² × 7
13. 13.How many factors does 39 have? (a) 5 (b) 4 (c) 2 (d) 3
14. 14.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7²
15. 15.What is the prime factorisation of 420? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2² × 3 × 5 × 7
16. 16.How many factors does 98 have? (a) 5 (b) 7 (c) 4 (d) 6
17. 17.How many factors does 29 have? (a) 3 (b) 2 (c) 1 (d) 4
18. 18.What is the smallest prime factor of 69? (a) 23 (b) 3 (c) 2 (d) 1
19. 19.What is the prime factorisation of 105? (a) 3³ × 5 × 7 (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3 × 5 × 7²
20. 20.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5 (c) 3 × 5² (d) 3² × 5
21. 21.How many factors does 104 have? (a) 9 (b) 8 (c) 6 (d) 7
22. 22.What is the smallest prime factor of 95? (a) 19 (b) 2 (c) 1 (d) 5
23. 23.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
24. 24.What is the smallest prime factor of 187? (a) 17 (b) 1 (c) 11 (d) 2
25. 25.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 3 (d) 1
26. 26.How many factors does 62 have? (a) 2 (b) 4 (c) 5 (d) 3
27. 27.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 1 (d) 13
28. 28.What is the smallest prime factor of 65? (a) 1 (b) 5 (c) 13 (d) 2
29. 29.How many factors does 65 have? (a) 2 (b) 3 (c) 5 (d) 4
30. 30.How many factors does 89 have? (a) 4 (b) 3 (c) 2 (d) 1
31. 31.How many factors does 79 have? (a) 4 (b) 1 (c) 3 (d) 2
32. 32.How many prime numbers are there between 80 and 100? (a) 3 (b) 4 (c) 2 (d) 5
33. 33.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3 × 5² (d) 3³ × 5
34. 34.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 8 (d) 7
35. 35.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
36. 36.What is the smallest prime factor of 77? (a) 7 (b) 2 (c) 1 (d) 11
37. 37.What is the prime factorisation of 315? (a) 3 × 5 × 7² (b) 3 × 5 × 7 (c) 3² × 5 × 7 (d) 3³ × 5 × 7
38. 38.What is the smallest prime factor of 155? (a) 1 (b) 2 (c) 31 (d) 5
39. 39.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 7 (d) 6
40. 40.How many factors does 63 have? (a) 5 (b) 7 (c) 4 (d) 6

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