Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 119 · 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 57? (a) 19 (b) 1 (c) 3 (d) 2
2. 2.How many factors does 46 have? (a) 4 (b) 5 (c) 3 (d) 2
3. 3.What is the smallest prime factor of 87? (a) 2 (b) 1 (c) 29 (d) 3
4. 4.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁵ × 7
5. 5.What is the smallest prime factor of 49? (a) 3 (b) 2 (c) 1 (d) 7
6. 6.How many factors does 63 have? (a) 5 (b) 4 (c) 7 (d) 6
7. 7.How many prime numbers are there between 20 and 30? (a) 2 (b) 4 (c) 1 (d) 3
8. 8.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 4 (d) 6
9. 9.How many factors does 116 have? (a) 5 (b) 6 (c) 7 (d) 4
10. 10.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5
11. 11.What is the prime factorisation of 63? (a) 3² × 7 (b) 3³ × 7 (c) 3 × 7 (d) 3 × 7²
12. 12.How many prime numbers are there between 20 and 50? (a) 8 (b) 9 (c) 6 (d) 7
13. 13.What is the smallest prime factor of 77? (a) 11 (b) 1 (c) 7 (d) 2
14. 14.How many prime numbers are there between 70 and 80? (a) 4 (b) 3 (c) 5 (d) 2
15. 15.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 3 (d) 4
16. 16.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2³ × 3 × 5 (d) 2⁴ × 3 × 5
17. 17.What is the smallest prime factor of 93? (a) 3 (b) 31 (c) 2 (d) 1
18. 18.How many prime numbers are there between 60 and 90? (a) 7 (b) 9 (c) 6 (d) 8
19. 19.How many prime numbers are there between 70 and 100? (a) 8 (b) 7 (c) 5 (d) 6
20. 20.How many factors does 109 have? (a) 2 (b) 4 (c) 1 (d) 3
21. 21.How many factors does 84 have? (a) 10 (b) 13 (c) 11 (d) 12
22. 22.How many factors does 22 have? (a) 3 (b) 2 (c) 5 (d) 4
23. 23.How many prime numbers are there between 40 and 60? (a) 4 (b) 7 (c) 5 (d) 6
24. 24.How many prime numbers are there between 30 and 40? (a) 3 (b) 2 (c) 1 (d) 4
25. 25.How many factors does 75 have? (a) 5 (b) 6 (c) 4 (d) 7
26. 26.What is the prime factorisation of 35? (a) 5³ × 7 (b) 5² × 7 (c) 5 × 7² (d) 5 × 7
27. 27.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
28. 28.What is the smallest prime factor of 299? (a) 23 (b) 2 (c) 13 (d) 1
29. 29.What is the prime factorisation of 18? (a) 2 × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2² × 3
30. 30.How many factors does 81 have? (a) 6 (b) 3 (c) 5 (d) 4
31. 31.How many factors does 29 have? (a) 1 (b) 3 (c) 4 (d) 2
32. 32.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 7 (d) 8
33. 33.How many factors does 83 have? (a) 2 (b) 4 (c) 3 (d) 1
34. 34.How many factors does 95 have? (a) 4 (b) 2 (c) 3 (d) 5
35. 35.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7 (d) 2 × 3 × 7²
36. 36.How many factors does 44 have? (a) 4 (b) 7 (c) 5 (d) 6
37. 37.How many factors does 42 have? (a) 6 (b) 7 (c) 8 (d) 9
38. 38.How many factors does 16 have? (a) 5 (b) 4 (c) 3 (d) 6
39. 39.What is the prime factorisation of 20? (a) 2 × 5 (b) 2 × 5² (c) 2³ × 5 (d) 2² × 5
40. 40.How many prime numbers are there between 90 and 120? (a) 5 (b) 7 (c) 6 (d) 8

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