Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 124 · 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 169? (a) 13 (b) 2 (c) 1 (d) 3
2. 2.How many factors does 13 have? (a) 4 (b) 1 (c) 3 (d) 2
3. 3.What is the smallest prime factor of 319? (a) 2 (b) 11 (c) 1 (d) 29
4. 4.How many prime numbers are there between 80 and 90? (a) 2 (b) 3 (c) 1 (d) 4
5. 5.What is the smallest prime factor of 119? (a) 17 (b) 7 (c) 1 (d) 2
6. 6.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
7. 7.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 2 (d) 4
8. 8.How many prime numbers are there between 40 and 70? (a) 9 (b) 8 (c) 7 (d) 6
9. 9.How many factors does 104 have? (a) 6 (b) 8 (c) 9 (d) 7
10. 10.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2 × 3 × 5³ (c) 2³ × 3 × 5 (d) 2² × 3 × 5
11. 11.How many factors does 41 have? (a) 4 (b) 3 (c) 1 (d) 2
12. 12.What is the smallest prime factor of 143? (a) 13 (b) 11 (c) 1 (d) 2
13. 13.How many factors does 83 have? (a) 3 (b) 1 (c) 4 (d) 2
14. 14.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 2 (d) 7
15. 15.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
16. 16.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
17. 17.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
18. 18.What is the smallest prime factor of 299? (a) 2 (b) 13 (c) 1 (d) 23
19. 19.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
20. 20.What is the prime factorisation of 28? (a) 2 × 7² (b) 2² × 7 (c) 2 × 7 (d) 2³ × 7
21. 21.How many factors does 15 have? (a) 2 (b) 3 (c) 4 (d) 5
22. 22.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2⁴ × 3 (c) 2² × 3 (d) 2 × 3³
23. 23.How many factors does 20 have? (a) 7 (b) 4 (c) 5 (d) 6
24. 24.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 1 (d) 5
25. 25.What is the smallest prime factor of 65? (a) 2 (b) 13 (c) 5 (d) 1
26. 26.What is the prime factorisation of 35? (a) 5 × 7² (b) 5³ × 7 (c) 5² × 7 (d) 5 × 7
27. 27.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
28. 28.How many factors does 87 have? (a) 5 (b) 4 (c) 3 (d) 2
29. 29.How many prime numbers are there between 10 and 40? (a) 9 (b) 7 (c) 10 (d) 8
30. 30.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5 (c) 2³ × 5 (d) 2 × 5²
31. 31.What is the prime factorisation of 40? (a) 2² × 5 (b) 2⁴ × 5 (c) 2 × 5³ (d) 2³ × 5
32. 32.How many prime numbers are there between 80 and 100? (a) 4 (b) 5 (c) 2 (d) 3
33. 33.How many prime numbers are there between 50 and 70? (a) 5 (b) 6 (c) 4 (d) 3
34. 34.How many factors does 70 have? (a) 7 (b) 8 (c) 9 (d) 6
35. 35.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2 × 3² × 7²
36. 36.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
37. 37.What is the smallest prime factor of 33? (a) 1 (b) 2 (c) 11 (d) 3
38. 38.How many prime numbers are there between 40 and 50? (a) 5 (b) 2 (c) 3 (d) 4
39. 39.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7² (c) 2 × 3 × 7 (d) 2² × 3 × 7
40. 40.What is the smallest prime factor of 49? (a) 7 (b) 1 (c) 2 (d) 3

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