Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 146 · 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.Which of these numbers divides exactly by 4? (a) 8315 (b) 3082 (c) 9745 (d) 3148
2. 2.What is the smallest number you must take away from 659 so that it divides exactly by 13?
3. 3.Which of these numbers divides exactly by 9? (a) 2335 (b) 6302 (c) 4974 (d) 9900
4. 4.How many factors does 22 have?
5. 5.What is the smallest number you must add to 311 so that it divides exactly by 4?
6. 6.Which of these numbers divides exactly by 9? (a) 8186 (b) 7659 (c) 3489 (d) 6321
7. 7.What is the smallest number you must add to 195 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 385 so that it divides exactly by 6?
9. 9.Which of these numbers divides exactly by 6? (a) 8838 (b) 7558 (c) 6043 (d) 3340
10. 10.What is the smallest number you must add to 915 so that it divides exactly by 8?
11. 11.Which of these numbers divides exactly by 11? (a) 4598 (b) 3187 (c) 3231 (d) 6987
12. 12.What is the smallest number you must take away from 652 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 638 so that it divides exactly by 13?
14. 14.How many factors does 35 have?
15. 15.Which of these numbers divides exactly by 4? (a) 2754 (b) 4825 (c) 3028 (d) 5674
16. 16.What is the smallest number you must take away from 290 so that it divides exactly by 4?
17. 17.How many factors does 12 have?
18. 18.How many factors does 49 have?
19. 19.How many factors does 86 have?
20. 20.How many factors does 79 have?
21. 21.What is the smallest number you must add to 241 so that it divides exactly by 4?
22. 22.How many factors does 37 have?
23. 23.Which of these numbers divides exactly by 9? (a) 8928 (b) 8023 (c) 4811 (d) 6613
24. 24.How many factors does 83 have?
25. 25.How many factors does 91 have?
26. 26.What is the smallest number you must take away from 425 so that it divides exactly by 11?
27. 27.What is the smallest number you must add to 335 so that it divides exactly by 13?
28. 28.Which of these numbers divides exactly by 6? (a) 7866 (b) 7397 (c) 6027 (d) 8445
29. 29.What is the smallest number you must take away from 658 so that it divides exactly by 4?
30. 30.Which of these numbers divides exactly by 3? (a) 4810 (b) 5792 (c) 6736 (d) 3411
31. 31.What is the smallest number you must add to 373 so that it divides exactly by 8?
32. 32.What is the smallest number you must add to 307 so that it divides exactly by 8?
33. 33.What is the smallest number you must add to 799 so that it divides exactly by 13?
34. 34.What is the smallest number you must add to 366 so that it divides exactly by 7?
35. 35.What is the smallest number you must take away from 545 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 3? (a) 3279 (b) 1058 (c) 1178 (d) 2968
37. 37.What is the smallest number you must take away from 845 so that it divides exactly by 12?
38. 38.What is the smallest number you must add to 845 so that it divides exactly by 3?
39. 39.What is the smallest number you must add to 238 so that it divides exactly by 8?
40. 40.Which of these numbers divides exactly by 6? (a) 2528 (b) 4717 (c) 2770 (d) 2688

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