Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 27 · 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 11? (a) 5671 (b) 5628 (c) 8808 (d) 3916
2. 2.Which of these numbers divides exactly by 11? (a) 2915 (b) 6929 (c) 3611 (d) 8600
3. 3.How many factors does 43 have?
4. 4.What is the smallest number you must add to 358 so that it divides exactly by 3?
5. 5.Which of these numbers divides exactly by 6? (a) 9745 (b) 8108 (c) 6545 (d) 5070
6. 6.Which of these numbers divides exactly by 3? (a) 1616 (b) 4141 (c) 5097 (d) 1474
7. 7.What is the smallest number you must add to 409 so that it divides exactly by 12?
8. 8.What is the smallest number you must add to 676 so that it divides exactly by 3?
9. 9.What is the smallest number you must take away from 425 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 866 so that it divides exactly by 9?
11. 11.What is the smallest number you must add to 567 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 342 so that it divides exactly by 7?
13. 13.How many factors does 41 have?
14. 14.What is the smallest number you must add to 305 so that it divides exactly by 12?
15. 15.Which of these numbers divides exactly by 3? (a) 8421 (b) 6118 (c) 1151 (d) 9592
16. 16.What is the smallest number you must take away from 487 so that it divides exactly by 6?
17. 17.What is the smallest number you must add to 982 so that it divides exactly by 11?
18. 18.What is the smallest number you must take away from 220 so that it divides exactly by 6?
19. 19.What is the smallest number you must add to 897 so that it divides exactly by 4?
20. 20.What is the smallest number you must take away from 961 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 230 so that it divides exactly by 4?
22. 22.What is the smallest number you must add to 120 so that it divides exactly by 13?
23. 23.Which of these numbers divides exactly by 9? (a) 5896 (b) 5025 (c) 4763 (d) 7191
24. 24.What is the smallest number you must take away from 519 so that it divides exactly by 11?
25. 25.How many factors does 13 have?
26. 26.What is the smallest number you must add to 669 so that it divides exactly by 9?
27. 27.How many factors does 76 have?
28. 28.How many factors does 19 have?
29. 29.How many factors does 46 have?
30. 30.What is the smallest number you must add to 319 so that it divides exactly by 9?
31. 31.Which of these numbers divides exactly by 4? (a) 1865 (b) 7873 (c) 6685 (d) 9808
32. 32.How many factors does 86 have?
33. 33.What is the smallest number you must take away from 849 so that it divides exactly by 11?
34. 34.How many factors does 57 have?
35. 35.What is the smallest number you must take away from 222 so that it divides exactly by 7?
36. 36.What is the smallest number you must add to 470 so that it divides exactly by 12?
37. 37.Which of these numbers divides exactly by 4? (a) 7861 (b) 7109 (c) 4506 (d) 9512
38. 38.What is the smallest number you must add to 109 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 3? (a) 6586 (b) 1143 (c) 8896 (d) 2152
40. 40.Which of these numbers divides exactly by 11? (a) 4934 (b) 1375 (c) 8260 (d) 4877

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