Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 29 · 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 66 have?
2. 2.Which of these numbers divides exactly by 6? (a) 7642 (b) 1669 (c) 3755 (d) 6900
3. 3.What is the smallest number you must add to 287 so that it divides exactly by 12?
4. 4.What is the smallest number you must take away from 177 so that it divides exactly by 8?
5. 5.What is the smallest number you must add to 115 so that it divides exactly by 6?
6. 6.How many factors does 19 have?
7. 7.How many factors does 26 have?
8. 8.What is the smallest number you must add to 695 so that it divides exactly by 3?
9. 9.Which of these numbers divides exactly by 9? (a) 7193 (b) 7708 (c) 5983 (d) 4590
10. 10.What is the smallest number you must add to 291 so that it divides exactly by 7?
11. 11.What is the smallest number you must add to 689 so that it divides exactly by 4?
12. 12.What is the smallest number you must add to 777 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 217 so that it divides exactly by 13?
14. 14.How many factors does 53 have?
15. 15.Which of these numbers divides exactly by 8? (a) 6117 (b) 4938 (c) 4055 (d) 8216
16. 16.How many factors does 99 have?
17. 17.What is the smallest number you must take away from 776 so that it divides exactly by 12?
18. 18.Which of these numbers divides exactly by 8? (a) 2585 (b) 8136 (c) 9178 (d) 2730
19. 19.What is the smallest number you must take away from 713 so that it divides exactly by 4?
20. 20.Which of these numbers divides exactly by 11? (a) 2959 (b) 2554 (c) 2736 (d) 4109
21. 21.What is the smallest number you must add to 281 so that it divides exactly by 8?
22. 22.How many factors does 93 have?
23. 23.What is the smallest number you must add to 211 so that it divides exactly by 6?
24. 24.What is the smallest number you must take away from 492 so that it divides exactly by 13?
25. 25.How many factors does 48 have?
26. 26.What is the smallest number you must add to 778 so that it divides exactly by 7?
27. 27.Which of these numbers divides exactly by 11? (a) 1162 (b) 8463 (c) 4858 (d) 2574
28. 28.What is the smallest number you must add to 742 so that it divides exactly by 6?
29. 29.How many factors does 45 have?
30. 30.What is the smallest number you must add to 993 so that it divides exactly by 13?
31. 31.How many factors does 27 have?
32. 32.What is the smallest number you must take away from 603 so that it divides exactly by 8?
33. 33.What is the smallest number you must take away from 755 so that it divides exactly by 11?
34. 34.How many factors does 98 have?
35. 35.Which of these numbers divides exactly by 8? (a) 3004 (b) 2805 (c) 1898 (d) 5264
36. 36.What is the smallest number you must take away from 833 so that it divides exactly by 8?
37. 37.What is the smallest number you must add to 729 so that it divides exactly by 11?
38. 38.What is the smallest number you must add to 249 so that it divides exactly by 12?
39. 39.How many factors does 87 have?
40. 40.What is the smallest number you must add to 626 so that it divides exactly by 3?

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