Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 19 · 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 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2 × 3 × 5 (d) 2³ × 3 × 5
2. 2.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 1 (d) 31
3. 3.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2 × 7² (c) 2 × 7 (d) 2² × 7
4. 4.How many prime numbers are there between 60 and 90? (a) 7 (b) 9 (c) 8 (d) 6
5. 5.What is the smallest prime factor of 121? (a) 1 (b) 3 (c) 2 (d) 11
6. 6.What is the smallest prime factor of 133? (a) 7 (b) 1 (c) 19 (d) 2
7. 7.How many factors does 99 have? (a) 4 (b) 6 (c) 7 (d) 5
8. 8.How many factors does 32 have? (a) 6 (b) 7 (c) 5 (d) 4
9. 9.What is the smallest prime factor of 203? (a) 1 (b) 7 (c) 29 (d) 2
10. 10.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
11. 11.How many prime numbers are there between 30 and 50? (a) 4 (b) 7 (c) 5 (d) 6
12. 12.What is the prime factorisation of 15? (a) 3 × 5² (b) 3² × 5 (c) 3 × 5 (d) 3³ × 5
13. 13.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 2 (d) 13
14. 14.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2² × 3² × 5 (d) 2³ × 3² × 5
15. 15.How many prime numbers are there between 60 and 80? (a) 5 (b) 6 (c) 4 (d) 7
16. 16.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2³ × 3 × 7 (d) 2⁵ × 3 × 7
17. 17.How many factors does 41 have? (a) 2 (b) 3 (c) 4 (d) 1
18. 18.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁴ × 3² (c) 2⁵ × 3² (d) 2² × 3⁴
19. 19.How many factors does 63 have? (a) 7 (b) 4 (c) 5 (d) 6
20. 20.How many prime numbers are there between 90 and 110? (a) 6 (b) 4 (c) 7 (d) 5
21. 21.What is the smallest prime factor of 247? (a) 13 (b) 1 (c) 2 (d) 19
22. 22.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁴ × 7
23. 23.How many factors does 89 have? (a) 3 (b) 4 (c) 2 (d) 1
24. 24.How many factors does 66 have? (a) 6 (b) 9 (c) 7 (d) 8
25. 25.What is the prime factorisation of 60? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
26. 26.What is the prime factorisation of 45? (a) 3 × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3² × 5
27. 27.What is the prime factorisation of 40? (a) 2³ × 5 (b) 2⁴ × 5 (c) 2² × 5 (d) 2 × 5³
28. 28.How many factors does 74 have? (a) 5 (b) 2 (c) 4 (d) 3
29. 29.How many factors does 97 have? (a) 4 (b) 3 (c) 2 (d) 1
30. 30.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁵ × 3 × 5 (d) 2 × 3 × 5⁴
31. 31.How many prime numbers are there between 30 and 40? (a) 2 (b) 3 (c) 1 (d) 4
32. 32.What is the smallest prime factor of 85? (a) 5 (b) 17 (c) 2 (d) 1
33. 33.How many factors does 45 have? (a) 6 (b) 4 (c) 7 (d) 5
34. 34.What is the prime factorisation of 56? (a) 2² × 7 (b) 2⁴ × 7 (c) 2 × 7³ (d) 2³ × 7
35. 35.How many factors does 77 have? (a) 4 (b) 2 (c) 3 (d) 5
36. 36.How many factors does 118 have? (a) 4 (b) 2 (c) 5 (d) 3
37. 37.What is the smallest prime factor of 115? (a) 23 (b) 1 (c) 2 (d) 5
38. 38.How many factors does 36 have? (a) 8 (b) 9 (c) 7 (d) 10
39. 39.How many prime numbers are there between 40 and 70? (a) 7 (b) 9 (c) 6 (d) 8
40. 40.How many factors does 116 have? (a) 7 (b) 5 (c) 6 (d) 4

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