Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 259 · 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 94 have?
2. 2.Which of these numbers divides exactly by 6? (a) 7721 (b) 9603 (c) 8859 (d) 2046
3. 3.Which of these numbers divides exactly by 4? (a) 7555 (b) 2002 (c) 4376 (d) 4922
4. 4.How many factors does 29 have?
5. 5.How many factors does 51 have?
6. 6.What is the smallest number you must add to 152 so that it divides exactly by 6?
7. 7.What is the smallest number you must add to 274 so that it divides exactly by 4?
8. 8.How many factors does 71 have?
9. 9.Which of these numbers divides exactly by 9? (a) 7011 (b) 4871 (c) 2343 (d) 3329
10. 10.What is the smallest number you must add to 252 so that it divides exactly by 13?
11. 11.Which of these numbers divides exactly by 9? (a) 7069 (b) 7983 (c) 2996 (d) 6252
12. 12.How many factors does 56 have?
13. 13.Which of these numbers divides exactly by 4? (a) 9592 (b) 5351 (c) 8321 (d) 9586
14. 14.What is the smallest number you must take away from 475 so that it divides exactly by 11?
15. 15.What is the smallest number you must add to 637 so that it divides exactly by 4?
16. 16.How many factors does 26 have?
17. 17.What is the smallest number you must take away from 365 so that it divides exactly by 3?
18. 18.What is the smallest number you must add to 967 so that it divides exactly by 8?
19. 19.What is the smallest number you must add to 269 so that it divides exactly by 3?
20. 20.What is the smallest number you must add to 989 so that it divides exactly by 6?
21. 21.What is the smallest number you must take away from 810 so that it divides exactly by 4?
22. 22.Which of these numbers divides exactly by 11? (a) 7260 (b) 5196 (c) 7292 (d) 1882
23. 23.What is the smallest number you must take away from 177 so that it divides exactly by 8?
24. 24.Which of these numbers divides exactly by 3? (a) 9526 (b) 9769 (c) 8259 (d) 8842
25. 25.Which of these numbers divides exactly by 11? (a) 4548 (b) 5448 (c) 3395 (d) 2200
26. 26.What is the smallest number you must take away from 454 so that it divides exactly by 13?
27. 27.What is the smallest number you must add to 749 so that it divides exactly by 3?
28. 28.How many factors does 50 have?
29. 29.What is the smallest number you must add to 179 so that it divides exactly by 8?
30. 30.Which of these numbers divides exactly by 6? (a) 1544 (b) 2697 (c) 8253 (d) 1776
31. 31.What is the smallest number you must add to 130 so that it divides exactly by 3?
32. 32.What is the smallest number you must take away from 244 so that it divides exactly by 9?
33. 33.What is the smallest number you must take away from 928 so that it divides exactly by 11?
34. 34.How many factors does 52 have?
35. 35.What is the smallest number you must take away from 940 so that it divides exactly by 7?
36. 36.How many factors does 32 have?
37. 37.How many factors does 64 have?
38. 38.Which of these numbers divides exactly by 9? (a) 3312 (b) 8605 (c) 2002 (d) 3451
39. 39.What is the smallest number you must take away from 631 so that it divides exactly by 13?
40. 40.What is the smallest number you must add to 593 so that it divides exactly by 11?

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