Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 287 · 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 449 so that it divides exactly by 12?
2. 2.What is the smallest number you must take away from 461 so that it divides exactly by 7?
3. 3.Which of these numbers divides exactly by 9? (a) 2213 (b) 7309 (c) 2081 (d) 6723
4. 4.What is the smallest number you must add to 836 so that it divides exactly by 7?
5. 5.Which of these numbers divides exactly by 3? (a) 8902 (b) 7612 (c) 8636 (d) 1230
6. 6.How many factors does 47 have?
7. 7.Which of these numbers divides exactly by 11? (a) 4196 (b) 2886 (c) 4753 (d) 1166
8. 8.Which of these numbers divides exactly by 11? (a) 4728 (b) 4489 (c) 1177 (d) 2974
9. 9.Which of these numbers divides exactly by 4? (a) 4483 (b) 2070 (c) 7848 (d) 4590
10. 10.How many factors does 29 have?
11. 11.What is the smallest number you must add to 907 so that it divides exactly by 3?
12. 12.Which of these numbers divides exactly by 9? (a) 1338 (b) 7128 (c) 6710 (d) 8972
13. 13.What is the smallest number you must add to 787 so that it divides exactly by 12?
14. 14.How many factors does 100 have?
15. 15.How many factors does 80 have?
16. 16.How many factors does 65 have?
17. 17.How many factors does 13 have?
18. 18.Which of these numbers divides exactly by 4? (a) 9958 (b) 6525 (c) 3148 (d) 8035
19. 19.What is the smallest number you must take away from 383 so that it divides exactly by 8?
20. 20.What is the smallest number you must add to 532 so that it divides exactly by 13?
21. 21.Which of these numbers divides exactly by 4? (a) 6517 (b) 7333 (c) 7403 (d) 4520
22. 22.What is the smallest number you must take away from 952 so that it divides exactly by 12?
23. 23.Which of these numbers divides exactly by 3? (a) 2086 (b) 2582 (c) 8619 (d) 4768
24. 24.How many factors does 55 have?
25. 25.Which of these numbers divides exactly by 8? (a) 5840 (b) 4859 (c) 6427 (d) 1558
26. 26.What is the smallest number you must take away from 359 so that it divides exactly by 6?
27. 27.How many factors does 81 have?
28. 28.What is the smallest number you must add to 910 so that it divides exactly by 11?
29. 29.Which of these numbers divides exactly by 4? (a) 8899 (b) 4261 (c) 6116 (d) 7239
30. 30.Which of these numbers divides exactly by 8? (a) 5695 (b) 5263 (c) 3768 (d) 5507
31. 31.What is the smallest number you must take away from 292 so that it divides exactly by 6?
32. 32.Which of these numbers divides exactly by 11? (a) 8159 (b) 5607 (c) 5632 (d) 5216
33. 33.What is the smallest number you must add to 529 so that it divides exactly by 6?
34. 34.How many factors does 90 have?
35. 35.How many factors does 39 have?
36. 36.How many factors does 93 have?
37. 37.Which of these numbers divides exactly by 3? (a) 1415 (b) 8630 (c) 1410 (d) 1522
38. 38.What is the smallest number you must add to 674 so that it divides exactly by 3?
39. 39.Which of these numbers divides exactly by 4? (a) 9385 (b) 7415 (c) 2360 (d) 9375
40. 40.Which of these numbers divides exactly by 8? (a) 7047 (b) 4326 (c) 1711 (d) 5408

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