Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 211 · 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 add to 271 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 581 so that it divides exactly by 6?
3. 3.What is the smallest number you must add to 587 so that it divides exactly by 3?
4. 4.How many factors does 14 have?
5. 5.How many factors does 19 have?
6. 6.What is the smallest number you must take away from 224 so that it divides exactly by 3?
7. 7.Which of these numbers divides exactly by 4? (a) 8419 (b) 1804 (c) 4869 (d) 6859
8. 8.Which of these numbers divides exactly by 3? (a) 3754 (b) 3703 (c) 7022 (d) 1986
9. 9.What is the smallest number you must take away from 883 so that it divides exactly by 9?
10. 10.Which of these numbers divides exactly by 11? (a) 1257 (b) 4929 (c) 9977 (d) 9659
11. 11.Which of these numbers divides exactly by 9? (a) 2116 (b) 5653 (c) 7481 (d) 1170
12. 12.How many factors does 76 have?
13. 13.Which of these numbers divides exactly by 8? (a) 8483 (b) 2776 (c) 2427 (d) 1434
14. 14.What is the smallest number you must take away from 727 so that it divides exactly by 6?
15. 15.How many factors does 55 have?
16. 16.How many factors does 83 have?
17. 17.What is the smallest number you must take away from 215 so that it divides exactly by 8?
18. 18.How many factors does 85 have?
19. 19.How many factors does 21 have?
20. 20.What is the smallest number you must take away from 771 so that it divides exactly by 11?
21. 21.Which of these numbers divides exactly by 4? (a) 5587 (b) 6553 (c) 3506 (d) 1076
22. 22.How many factors does 71 have?
23. 23.What is the smallest number you must add to 575 so that it divides exactly by 3?
24. 24.How many factors does 42 have?
25. 25.What is the smallest number you must add to 834 so that it divides exactly by 12?
26. 26.Which of these numbers divides exactly by 4? (a) 6385 (b) 9066 (c) 7328 (d) 8602
27. 27.What is the smallest number you must add to 923 so that it divides exactly by 8?
28. 28.Which of these numbers divides exactly by 3? (a) 2220 (b) 6653 (c) 1528 (d) 3979
29. 29.What is the smallest number you must add to 539 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 521 so that it divides exactly by 13?
31. 31.How many factors does 47 have?
32. 32.Which of these numbers divides exactly by 11? (a) 9201 (b) 4758 (c) 9174 (d) 9142
33. 33.Which of these numbers divides exactly by 11? (a) 5705 (b) 1549 (c) 5629 (d) 2541
34. 34.How many factors does 41 have?
35. 35.What is the smallest number you must take away from 598 so that it divides exactly by 3?
36. 36.Which of these numbers divides exactly by 8? (a) 8527 (b) 1996 (c) 2232 (d) 1849
37. 37.What is the smallest number you must add to 919 so that it divides exactly by 7?
38. 38.What is the smallest number you must take away from 766 so that it divides exactly by 7?
39. 39.What is the smallest number you must take away from 319 so that it divides exactly by 4?
40. 40.What is the smallest number you must take away from 347 so that it divides exactly by 6?

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