Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 141 · 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 143? (a) 2 (b) 11 (c) 1 (d) 13
2. 2.What is the smallest prime factor of 39? (a) 1 (b) 3 (c) 13 (d) 2
3. 3.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 3 (d) 1
4. 4.How many factors does 53 have? (a) 4 (b) 1 (c) 3 (d) 2
5. 5.How many prime numbers are there between 10 and 40? (a) 10 (b) 7 (c) 8 (d) 9
6. 6.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2² × 3⁴ (c) 2⁴ × 3² (d) 2⁵ × 3²
7. 7.How many prime numbers are there between 40 and 70? (a) 8 (b) 7 (c) 6 (d) 9
8. 8.How many factors does 17 have? (a) 1 (b) 4 (c) 2 (d) 3
9. 9.How many factors does 111 have? (a) 4 (b) 3 (c) 5 (d) 2
10. 10.How many prime numbers are there between 60 and 70? (a) 1 (b) 2 (c) 3 (d) 4
11. 11.How many factors does 52 have? (a) 5 (b) 6 (c) 4 (d) 7
12. 12.What is the smallest prime factor of 221? (a) 1 (b) 13 (c) 2 (d) 17
13. 13.What is the smallest prime factor of 217? (a) 2 (b) 1 (c) 7 (d) 31
14. 14.How many prime numbers are there between 10 and 20? (a) 5 (b) 4 (c) 3 (d) 6
15. 15.What is the prime factorisation of 72? (a) 2² × 3² (b) 2⁴ × 3² (c) 2² × 3³ (d) 2³ × 3²
16. 16.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 7 (d) 11
17. 17.What is the prime factorisation of 21? (a) 3 × 7² (b) 3² × 7 (c) 3³ × 7 (d) 3 × 7
18. 18.What is the prime factorisation of 252? (a) 2³ × 3² × 7 (b) 2 × 3² × 7² (c) 2 × 3² × 7 (d) 2² × 3² × 7
19. 19.What is the smallest prime factor of 247? (a) 1 (b) 19 (c) 13 (d) 2
20. 20.How many factors does 81 have? (a) 6 (b) 4 (c) 5 (d) 3
21. 21.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2³ × 3 (c) 2⁵ × 3 (d) 2⁴ × 3
22. 22.What is the prime factorisation of 42? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
23. 23.What is the prime factorisation of 504? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7³ (d) 2⁴ × 3² × 7
24. 24.How many factors does 31 have? (a) 1 (b) 4 (c) 3 (d) 2
25. 25.How many factors does 36 have? (a) 7 (b) 8 (c) 10 (d) 9
26. 26.How many factors does 75 have? (a) 6 (b) 7 (c) 4 (d) 5
27. 27.What is the prime factorisation of 63? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
28. 28.How many factors does 41 have? (a) 2 (b) 1 (c) 3 (d) 4
29. 29.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 6 (d) 8
30. 30.How many factors does 70 have? (a) 9 (b) 7 (c) 6 (d) 8
31. 31.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2 × 3² (d) 2³ × 3
32. 32.How many prime numbers are there between 10 and 30? (a) 7 (b) 5 (c) 8 (d) 6
33. 33.How many prime numbers are there between 40 and 60? (a) 4 (b) 6 (c) 7 (d) 5
34. 34.What is the smallest prime factor of 145? (a) 5 (b) 29 (c) 2 (d) 1
35. 35.How many prime numbers are there between 30 and 40? (a) 4 (b) 1 (c) 3 (d) 2
36. 36.What is the prime factorisation of 140? (a) 2³ × 5 × 7 (b) 2 × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
37. 37.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 13 (d) 7
38. 38.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2 × 3³ (c) 2² × 3 (d) 2³ × 3
39. 39.How many factors does 48 have? (a) 9 (b) 8 (c) 10 (d) 11
40. 40.How many prime numbers are there between 70 and 90? (a) 5 (b) 4 (c) 6 (d) 7

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