Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 82 · 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 50 have? (a) 4 (b) 6 (c) 5 (d) 7
2. 2.How many factors does 20 have? (a) 6 (b) 7 (c) 5 (d) 4
3. 3.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 2 (d) 5
4. 4.How many prime numbers are there between 30 and 40? (a) 2 (b) 4 (c) 1 (d) 3
5. 5.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2⁵ × 3 (c) 2⁴ × 3 (d) 2 × 3⁴
6. 6.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
7. 7.How many factors does 19 have? (a) 1 (b) 4 (c) 2 (d) 3
8. 8.What is the prime factorisation of 45? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
9. 9.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2² × 3³ (c) 2² × 3² (d) 2 × 3²
10. 10.How many prime numbers are there between 40 and 60? (a) 7 (b) 5 (c) 6 (d) 4
11. 11.What is the smallest prime factor of 299? (a) 2 (b) 1 (c) 13 (d) 23
12. 12.How many prime numbers are there between 70 and 90? (a) 6 (b) 4 (c) 7 (d) 5
13. 13.How many prime numbers are there between 40 and 50? (a) 3 (b) 2 (c) 4 (d) 5
14. 14.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2⁴ × 3 (d) 2³ × 3
15. 15.How many prime numbers are there between 10 and 40? (a) 8 (b) 7 (c) 10 (d) 9
16. 16.What is the smallest prime factor of 93? (a) 31 (b) 2 (c) 1 (d) 3
17. 17.What is the prime factorisation of 90? (a) 2 × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2³ × 3² × 5
18. 18.How many factors does 62 have? (a) 5 (b) 2 (c) 4 (d) 3
19. 19.How many prime numbers are there between 60 and 90? (a) 8 (b) 7 (c) 6 (d) 9
20. 20.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7³ (d) 2³ × 3² × 7
21. 21.How many factors does 64 have? (a) 7 (b) 5 (c) 6 (d) 8
22. 22.How many factors does 14 have? (a) 2 (b) 3 (c) 5 (d) 4
23. 23.How many factors does 48 have? (a) 11 (b) 9 (c) 10 (d) 8
24. 24.What is the smallest prime factor of 203? (a) 2 (b) 7 (c) 29 (d) 1
25. 25.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
26. 26.How many prime numbers are there between 30 and 50? (a) 5 (b) 6 (c) 7 (d) 4
27. 27.How many prime numbers are there between 20 and 30? (a) 1 (b) 4 (c) 3 (d) 2
28. 28.How many factors does 55 have? (a) 4 (b) 2 (c) 3 (d) 5
29. 29.How many factors does 71 have? (a) 2 (b) 4 (c) 3 (d) 1
30. 30.How many factors does 112 have? (a) 11 (b) 10 (c) 8 (d) 9
31. 31.What is the prime factorisation of 315? (a) 3² × 5 × 7 (b) 3 × 5 × 7 (c) 3 × 5 × 7² (d) 3³ × 5 × 7
32. 32.How many prime numbers are there between 60 and 80? (a) 4 (b) 7 (c) 5 (d) 6
33. 33.How many prime numbers are there between 70 and 100? (a) 8 (b) 6 (c) 5 (d) 7
34. 34.How many factors does 109 have? (a) 2 (b) 1 (c) 3 (d) 4
35. 35.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁵ × 5 × 7 (c) 2⁴ × 5 × 7 (d) 2³ × 5 × 7
36. 36.How many factors does 100 have? (a) 10 (b) 9 (c) 8 (d) 7
37. 37.What is the prime factorisation of 14? (a) 2 × 7² (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7
38. 38.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2 × 7³ (c) 2² × 7 (d) 2³ × 7
39. 39.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
40. 40.How many factors does 13 have? (a) 2 (b) 4 (c) 1 (d) 3

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