Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 250 · 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.What is the smallest number you must take away from 788 so that it divides exactly by 9?
2. 2.How many factors does 71 have?
3. 3.What is the smallest number you must take away from 206 so that it divides exactly by 13?
4. 4.Which of these numbers divides exactly by 4? (a) 9289 (b) 3651 (c) 4703 (d) 7016
5. 5.What is the smallest number you must add to 188 so that it divides exactly by 11?
6. 6.How many factors does 25 have?
7. 7.Which of these numbers divides exactly by 3? (a) 2435 (b) 9369 (c) 9542 (d) 1646
8. 8.How many factors does 88 have?
9. 9.What is the smallest number you must take away from 425 so that it divides exactly by 9?
10. 10.What is the smallest number you must add to 263 so that it divides exactly by 3?
11. 11.How many factors does 18 have?
12. 12.Which of these numbers divides exactly by 6? (a) 7278 (b) 1117 (c) 6841 (d) 5693
13. 13.Which of these numbers divides exactly by 3? (a) 3761 (b) 1208 (c) 1691 (d) 5571
14. 14.What is the smallest number you must add to 224 so that it divides exactly by 3?
15. 15.What is the smallest number you must add to 654 so that it divides exactly by 12?
16. 16.Which of these numbers divides exactly by 8? (a) 9931 (b) 9390 (c) 6108 (d) 7888
17. 17.What is the smallest number you must add to 739 so that it divides exactly by 12?
18. 18.Which of these numbers divides exactly by 9? (a) 5944 (b) 1702 (c) 6596 (d) 6372
19. 19.What is the smallest number you must add to 623 so that it divides exactly by 4?
20. 20.What is the smallest number you must take away from 833 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 328 so that it divides exactly by 11?
22. 22.What is the smallest number you must add to 557 so that it divides exactly by 7?
23. 23.Which of these numbers divides exactly by 8? (a) 2683 (b) 7207 (c) 1495 (d) 9840
24. 24.Which of these numbers divides exactly by 3? (a) 6504 (b) 5293 (c) 5149 (d) 1463
25. 25.How many factors does 66 have?
26. 26.What is the smallest number you must add to 267 so that it divides exactly by 6?
27. 27.Which of these numbers divides exactly by 9? (a) 4007 (b) 3235 (c) 1869 (d) 2610
28. 28.What is the smallest number you must add to 226 so that it divides exactly by 7?
29. 29.What is the smallest number you must take away from 955 so that it divides exactly by 12?
30. 30.What is the smallest number you must take away from 992 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 9? (a) 7692 (b) 7915 (c) 6012 (d) 6078
32. 32.Which of these numbers divides exactly by 8? (a) 8927 (b) 2146 (c) 7336 (d) 4987
33. 33.What is the smallest number you must add to 239 so that it divides exactly by 6?
34. 34.Which of these numbers divides exactly by 4? (a) 3202 (b) 7997 (c) 3664 (d) 9354
35. 35.Which of these numbers divides exactly by 4? (a) 1343 (b) 5398 (c) 3577 (d) 6580
36. 36.What is the smallest number you must take away from 769 so that it divides exactly by 13?
37. 37.What is the smallest number you must take away from 106 so that it divides exactly by 13?
38. 38.What is the smallest number you must add to 358 so that it divides exactly by 11?
39. 39.What is the smallest number you must add to 539 so that it divides exactly by 13?
40. 40.How many factors does 21 have?

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