Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 227 · 40 questions

The method (Rules and powers): By 3 or 9: the digit sum divides by 3 or 9. By 4: the last two digits. By 8: the last three digits. By 6: even and divisible by 3. By 11: the sums of alternate digits are equal or differ by 11. Number of factors: write n = p^a × q^b …, then the count is (a + 1) × (b + 1) × …. To make n divisible by d: divide, then add (d − remainder) or take away the remainder.

1. 1.How many factors does 67 have?
2. 2.What is the smallest number you must add to 368 so that it divides exactly by 11?
3. 3.Which of these numbers divides exactly by 11? (a) 5159 (b) 4837 (c) 1228 (d) 4289
4. 4.How many factors does 27 have?
5. 5.How many factors does 77 have?
6. 6.What is the smallest number you must add to 946 so that it divides exactly by 12?
7. 7.What is the smallest number you must add to 796 so that it divides exactly by 11?
8. 8.Which of these numbers divides exactly by 11? (a) 5085 (b) 6165 (c) 8707 (d) 5005
9. 9.What is the smallest number you must take away from 395 so that it divides exactly by 8?
10. 10.How many factors does 63 have?
11. 11.Which of these numbers divides exactly by 9? (a) 7972 (b) 6075 (c) 8450 (d) 9771
12. 12.What is the smallest number you must take away from 743 so that it divides exactly by 9?
13. 13.How many factors does 57 have?
14. 14.What is the smallest number you must take away from 816 so that it divides exactly by 11?
15. 15.What is the smallest number you must take away from 546 so that it divides exactly by 12?
16. 16.What is the smallest number you must take away from 751 so that it divides exactly by 6?
17. 17.What is the smallest number you must add to 122 so that it divides exactly by 3?
18. 18.What is the smallest number you must add to 147 so that it divides exactly by 12?
19. 19.How many factors does 31 have?
20. 20.Which of these numbers divides exactly by 3? (a) 2026 (b) 6762 (c) 7430 (d) 9212
21. 21.What is the smallest number you must take away from 845 so that it divides exactly by 8?
22. 22.What is the smallest number you must add to 146 so that it divides exactly by 7?
23. 23.How many factors does 92 have?
24. 24.How many factors does 35 have?
25. 25.What is the smallest number you must take away from 312 so that it divides exactly by 7?
26. 26.What is the smallest number you must take away from 297 so that it divides exactly by 6?
27. 27.What is the smallest number you must add to 562 so that it divides exactly by 7?
28. 28.What is the smallest number you must take away from 380 so that it divides exactly by 11?
29. 29.How many factors does 54 have?
30. 30.What is the smallest number you must take away from 311 so that it divides exactly by 3?
31. 31.Which of these numbers divides exactly by 6? (a) 2537 (b) 9696 (c) 8407 (d) 6074
32. 32.Which of these numbers divides exactly by 11? (a) 5346 (b) 1767 (c) 1706 (d) 1761
33. 33.Which of these numbers divides exactly by 3? (a) 4936 (b) 4552 (c) 3311 (d) 8535
34. 34.Which of these numbers divides exactly by 9? (a) 7837 (b) 1735 (c) 2025 (d) 3391
35. 35.How many factors does 47 have?
36. 36.What is the smallest number you must take away from 427 so that it divides exactly by 12?
37. 37.What is the smallest number you must add to 536 so that it divides exactly by 6?
38. 38.What is the smallest number you must add to 557 so that it divides exactly by 6?
39. 39.What is the smallest number you must add to 719 so that it divides exactly by 8?
40. 40.Which of these numbers divides exactly by 4? (a) 7321 (b) 2567 (c) 3915 (d) 9912

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