Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 33 · 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 288 so that it divides exactly by 11?
2. 2.Which of these numbers divides exactly by 3? (a) 3587 (b) 2152 (c) 1719 (d) 6454
3. 3.What is the smallest number you must take away from 469 so that it divides exactly by 6?
4. 4.Which of these numbers divides exactly by 11? (a) 8956 (b) 8721 (c) 8230 (d) 9658
5. 5.What is the smallest number you must add to 862 so that it divides exactly by 8?
6. 6.What is the smallest number you must add to 477 so that it divides exactly by 6?
7. 7.Which of these numbers divides exactly by 4? (a) 1990 (b) 4293 (c) 9782 (d) 1440
8. 8.Which of these numbers divides exactly by 6? (a) 8913 (b) 7170 (c) 3635 (d) 6457
9. 9.What is the smallest number you must take away from 324 so that it divides exactly by 11?
10. 10.Which of these numbers divides exactly by 8? (a) 8108 (b) 4899 (c) 1934 (d) 1248
11. 11.How many factors does 24 have?
12. 12.Which of these numbers divides exactly by 11? (a) 1209 (b) 7713 (c) 9031 (d) 2554
13. 13.Which of these numbers divides exactly by 8? (a) 9418 (b) 3216 (c) 1670 (d) 2323
14. 14.What is the smallest number you must add to 514 so that it divides exactly by 11?
15. 15.What is the smallest number you must take away from 695 so that it divides exactly by 9?
16. 16.What is the smallest number you must take away from 691 so that it divides exactly by 6?
17. 17.What is the smallest number you must take away from 110 so that it divides exactly by 6?
18. 18.Which of these numbers divides exactly by 3? (a) 9608 (b) 7003 (c) 9195 (d) 5809
19. 19.How many factors does 71 have?
20. 20.How many factors does 33 have?
21. 21.How many factors does 42 have?
22. 22.Which of these numbers divides exactly by 8? (a) 5773 (b) 1524 (c) 7615 (d) 6320
23. 23.What is the smallest number you must take away from 129 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 893 so that it divides exactly by 13?
25. 25.How many factors does 72 have?
26. 26.What is the smallest number you must add to 123 so that it divides exactly by 13?
27. 27.What is the smallest number you must take away from 426 so that it divides exactly by 4?
28. 28.What is the smallest number you must take away from 290 so that it divides exactly by 4?
29. 29.How many factors does 50 have?
30. 30.Which of these numbers divides exactly by 11? (a) 4301 (b) 2419 (c) 1887 (d) 9491
31. 31.Which of these numbers divides exactly by 6? (a) 7854 (b) 8549 (c) 5486 (d) 8881
32. 32.Which of these numbers divides exactly by 9? (a) 5753 (b) 9729 (c) 9102 (d) 2768
33. 33.What is the smallest number you must take away from 105 so that it divides exactly by 9?
34. 34.How many factors does 58 have?
35. 35.What is the smallest number you must add to 877 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 674 so that it divides exactly by 8?
37. 37.What is the smallest number you must add to 974 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 585 so that it divides exactly by 6?
39. 39.How many factors does 90 have?
40. 40.What is the smallest number you must take away from 629 so that it divides exactly by 9?

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