Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 168 · 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 12 have? (a) 5 (b) 6 (c) 7 (d) 4
2. 2.How many factors does 93 have? (a) 2 (b) 3 (c) 5 (d) 4
3. 3.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 1 (d) 17
4. 4.What is the smallest prime factor of 143? (a) 11 (b) 13 (c) 1 (d) 2
5. 5.How many prime numbers are there between 20 and 50? (a) 9 (b) 6 (c) 7 (d) 8
6. 6.What is the smallest prime factor of 119? (a) 7 (b) 2 (c) 17 (d) 1
7. 7.How many factors does 13 have? (a) 1 (b) 3 (c) 2 (d) 4
8. 8.How many factors does 51 have? (a) 5 (b) 2 (c) 4 (d) 3
9. 9.How many prime numbers are there between 10 and 30? (a) 7 (b) 8 (c) 5 (d) 6
10. 10.How many prime numbers are there between 30 and 40? (a) 4 (b) 3 (c) 1 (d) 2
11. 11.How many factors does 36 have? (a) 7 (b) 10 (c) 9 (d) 8
12. 12.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2⁴ × 5 (c) 2³ × 5 (d) 2 × 5⁴
13. 13.How many prime numbers are there between 70 and 100? (a) 6 (b) 8 (c) 5 (d) 7
14. 14.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2 × 3² × 5 (d) 2³ × 3² × 5
15. 15.What is the prime factorisation of 280? (a) 2³ × 5 × 7 (b) 2⁴ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7³
16. 16.How many prime numbers are there between 40 and 60? (a) 7 (b) 4 (c) 6 (d) 5
17. 17.What is the prime factorisation of 56? (a) 2 × 7³ (b) 2³ × 7 (c) 2⁴ × 7 (d) 2² × 7
18. 18.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7² (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
19. 19.What is the prime factorisation of 60? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
20. 20.How many factors does 88 have? (a) 8 (b) 7 (c) 6 (d) 9
21. 21.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 3 (d) 2
22. 22.What is the prime factorisation of 14? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
23. 23.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 2 (d) 7
24. 24.How many factors does 46 have? (a) 3 (b) 2 (c) 4 (d) 5
25. 25.What is the prime factorisation of 240? (a) 2⁵ × 3 × 5 (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2 × 3 × 5⁴
26. 26.What is the smallest prime factor of 93? (a) 1 (b) 31 (c) 3 (d) 2
27. 27.How many prime numbers are there between 80 and 90? (a) 3 (b) 1 (c) 2 (d) 4
28. 28.What is the prime factorisation of 20? (a) 2 × 5 (b) 2² × 5 (c) 2 × 5² (d) 2³ × 5
29. 29.What is the prime factorisation of 336? (a) 2³ × 3 × 7 (b) 2⁵ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7⁴
30. 30.What is the smallest prime factor of 55? (a) 1 (b) 2 (c) 11 (d) 5
31. 31.What is the prime factorisation of 35? (a) 5 × 7² (b) 5 × 7 (c) 5² × 7 (d) 5³ × 7
32. 32.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 31 (d) 1
33. 33.What is the prime factorisation of 90? (a) 2² × 3² × 5 (b) 2³ × 3² × 5 (c) 2 × 3² × 5 (d) 2 × 3² × 5²
34. 34.What is the smallest prime factor of 95? (a) 2 (b) 5 (c) 19 (d) 1
35. 35.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
36. 36.How many prime numbers are there between 60 and 70? (a) 1 (b) 3 (c) 4 (d) 2
37. 37.How many factors does 42 have? (a) 9 (b) 6 (c) 8 (d) 7
38. 38.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
39. 39.What is the prime factorisation of 252? (a) 2 × 3² × 7 (b) 2 × 3² × 7² (c) 2² × 3² × 7 (d) 2³ × 3² × 7
40. 40.What is the smallest prime factor of 21? (a) 1 (b) 3 (c) 7 (d) 2

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