Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 172 · 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 prime numbers are there between 30 and 60? (a) 7 (b) 9 (c) 8 (d) 6
2. 2.What is the prime factorisation of 112? (a) 2⁵ × 7 (b) 2⁴ × 7 (c) 2 × 7⁴ (d) 2³ × 7
3. 3.How many prime numbers are there between 10 and 30? (a) 5 (b) 7 (c) 6 (d) 8
4. 4.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 6 (d) 7
5. 5.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2 × 3² × 7³ (c) 2⁴ × 3² × 7 (d) 2² × 3² × 7
6. 6.What is the smallest prime factor of 155? (a) 5 (b) 2 (c) 1 (d) 31
7. 7.What is the smallest prime factor of 119? (a) 17 (b) 2 (c) 7 (d) 1
8. 8.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7 (d) 2 × 7²
9. 9.What is the prime factorisation of 28? (a) 2 × 7 (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7²
10. 10.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁴ × 5 × 7 (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
11. 11.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2³ × 5 (d) 2 × 5²
12. 12.How many factors does 42 have? (a) 9 (b) 8 (c) 6 (d) 7
13. 13.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 4 (d) 3
14. 14.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2 × 3 × 7⁴ (d) 2⁴ × 3 × 7
15. 15.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 3 (d) 2
16. 16.What is the smallest prime factor of 341? (a) 1 (b) 31 (c) 11 (d) 2
17. 17.How many factors does 102 have? (a) 8 (b) 9 (c) 7 (d) 6
18. 18.What is the prime factorisation of 30? (a) 2 × 3 × 5² (b) 2² × 3 × 5 (c) 2 × 3 × 5 (d) 2³ × 3 × 5
19. 19.How many factors does 53 have? (a) 3 (b) 2 (c) 1 (d) 4
20. 20.What is the prime factorisation of 56? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7³ (d) 2⁴ × 7
21. 21.How many prime numbers are there between 30 and 50? (a) 7 (b) 6 (c) 5 (d) 4
22. 22.How many factors does 27 have? (a) 5 (b) 3 (c) 2 (d) 4
23. 23.How many factors does 12 have? (a) 7 (b) 5 (c) 6 (d) 4
24. 24.How many factors does 98 have? (a) 6 (b) 5 (c) 4 (d) 7
25. 25.How many prime numbers are there between 80 and 100? (a) 5 (b) 2 (c) 4 (d) 3
26. 26.What is the smallest prime factor of 145? (a) 2 (b) 5 (c) 29 (d) 1
27. 27.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
28. 28.What is the smallest prime factor of 91? (a) 2 (b) 7 (c) 1 (d) 13
29. 29.How many factors does 37 have? (a) 3 (b) 4 (c) 2 (d) 1
30. 30.How many factors does 25 have? (a) 2 (b) 1 (c) 3 (d) 4
31. 31.How many factors does 18 have? (a) 4 (b) 6 (c) 5 (d) 7
32. 32.What is the smallest prime factor of 33? (a) 3 (b) 1 (c) 2 (d) 11
33. 33.How many factors does 66 have? (a) 7 (b) 8 (c) 9 (d) 6
34. 34.How many prime numbers are there between 20 and 40? (a) 5 (b) 6 (c) 4 (d) 3
35. 35.What is the smallest prime factor of 299? (a) 2 (b) 23 (c) 13 (d) 1
36. 36.How many prime numbers are there between 50 and 60? (a) 3 (b) 1 (c) 4 (d) 2
37. 37.How many factors does 96 have? (a) 11 (b) 12 (c) 10 (d) 13
38. 38.What is the smallest prime factor of 21? (a) 1 (b) 2 (c) 7 (d) 3
39. 39.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2³ × 5 (c) 2⁴ × 5 (d) 2 × 5⁴
40. 40.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2³ × 3² × 7 (d) 2² × 3² × 7

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad