Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 243 · 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.How many factors does 28 have?
2. 2.What is the smallest number you must add to 173 so that it divides exactly by 12?
3. 3.What is the smallest number you must take away from 181 so that it divides exactly by 6?
4. 4.What is the smallest number you must take away from 509 so that it divides exactly by 13?
5. 5.Which of these numbers divides exactly by 4? (a) 4964 (b) 7433 (c) 9102 (d) 9053
6. 6.What is the smallest number you must add to 823 so that it divides exactly by 3?
7. 7.How many factors does 67 have?
8. 8.What is the smallest number you must take away from 353 so that it divides exactly by 7?
9. 9.How many factors does 87 have?
10. 10.Which of these numbers divides exactly by 11? (a) 8314 (b) 9457 (c) 9339 (d) 7364
11. 11.What is the smallest number you must add to 421 so that it divides exactly by 12?
12. 12.Which of these numbers divides exactly by 9? (a) 9643 (b) 4371 (c) 6816 (d) 5742
13. 13.What is the smallest number you must add to 749 so that it divides exactly by 3?
14. 14.What is the smallest number you must add to 259 so that it divides exactly by 9?
15. 15.What is the smallest number you must add to 536 so that it divides exactly by 12?
16. 16.How many factors does 26 have?
17. 17.What is the smallest number you must take away from 180 so that it divides exactly by 13?
18. 18.Which of these numbers divides exactly by 4? (a) 7230 (b) 1638 (c) 4845 (d) 6136
19. 19.How many factors does 77 have?
20. 20.What is the smallest number you must add to 560 so that it divides exactly by 13?
21. 21.What is the smallest number you must add to 148 so that it divides exactly by 8?
22. 22.Which of these numbers divides exactly by 8? (a) 1998 (b) 1096 (c) 4171 (d) 6522
23. 23.How many factors does 31 have?
24. 24.How many factors does 32 have?
25. 25.What is the smallest number you must add to 410 so that it divides exactly by 7?
26. 26.How many factors does 14 have?
27. 27.What is the smallest number you must take away from 286 so that it divides exactly by 8?
28. 28.How many factors does 57 have?
29. 29.Which of these numbers divides exactly by 9? (a) 3414 (b) 7101 (c) 5083 (d) 1803
30. 30.What is the smallest number you must take away from 987 so that it divides exactly by 13?
31. 31.Which of these numbers divides exactly by 6? (a) 9557 (b) 3382 (c) 5668 (d) 2748
32. 32.What is the smallest number you must add to 100 so that it divides exactly by 3?
33. 33.Which of these numbers divides exactly by 3? (a) 5521 (b) 2089 (c) 9026 (d) 5295
34. 34.How many factors does 36 have?
35. 35.What is the smallest number you must add to 152 so that it divides exactly by 13?
36. 36.Which of these numbers divides exactly by 3? (a) 4982 (b) 1559 (c) 9001 (d) 7893
37. 37.What is the smallest number you must take away from 661 so that it divides exactly by 9?
38. 38.Which of these numbers divides exactly by 6? (a) 2993 (b) 9105 (c) 1831 (d) 2844
39. 39.What is the smallest number you must add to 493 so that it divides exactly by 4?
40. 40.Which of these numbers divides exactly by 9? (a) 9486 (b) 2928 (c) 9750 (d) 3338

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