Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 57 · 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 4? (a) 8702 (b) 9597 (c) 5746 (d) 1660
2. 2.What is the smallest number you must add to 262 so that it divides exactly by 4?
3. 3.How many factors does 95 have?
4. 4.Which of these numbers divides exactly by 9? (a) 2480 (b) 2440 (c) 9464 (d) 8685
5. 5.What is the smallest number you must add to 367 so that it divides exactly by 3?
6. 6.How many factors does 43 have?
7. 7.What is the smallest number you must add to 817 so that it divides exactly by 12?
8. 8.What is the smallest number you must take away from 475 so that it divides exactly by 6?
9. 9.What is the smallest number you must add to 146 so that it divides exactly by 3?
10. 10.What is the smallest number you must take away from 535 so that it divides exactly by 4?
11. 11.What is the smallest number you must take away from 218 so that it divides exactly by 7?
12. 12.How many factors does 62 have?
13. 13.What is the smallest number you must take away from 454 so that it divides exactly by 6?
14. 14.What is the smallest number you must take away from 294 so that it divides exactly by 11?
15. 15.Which of these numbers divides exactly by 9? (a) 1161 (b) 2389 (c) 4135 (d) 1507
16. 16.What is the smallest number you must take away from 961 so that it divides exactly by 11?
17. 17.What is the smallest number you must take away from 746 so that it divides exactly by 7?
18. 18.Which of these numbers divides exactly by 3? (a) 9041 (b) 3105 (c) 1012 (d) 7394
19. 19.Which of these numbers divides exactly by 4? (a) 4625 (b) 1140 (c) 9706 (d) 8845
20. 20.What is the smallest number you must add to 631 so that it divides exactly by 11?
21. 21.What is the smallest number you must take away from 634 so that it divides exactly by 3?
22. 22.Which of these numbers divides exactly by 6? (a) 4664 (b) 5394 (c) 1103 (d) 3758
23. 23.What is the smallest number you must add to 147 so that it divides exactly by 12?
24. 24.Which of these numbers divides exactly by 8? (a) 5386 (b) 1696 (c) 7361 (d) 4250
25. 25.Which of these numbers divides exactly by 9? (a) 7803 (b) 2522 (c) 8828 (d) 1579
26. 26.How many factors does 30 have?
27. 27.What is the smallest number you must take away from 977 so that it divides exactly by 8?
28. 28.Which of these numbers divides exactly by 4? (a) 1357 (b) 1836 (c) 9761 (d) 3406
29. 29.Which of these numbers divides exactly by 4? (a) 3155 (b) 8803 (c) 1786 (d) 1912
30. 30.What is the smallest number you must take away from 699 so that it divides exactly by 6?
31. 31.How many factors does 75 have?
32. 32.Which of these numbers divides exactly by 3? (a) 2750 (b) 1063 (c) 6796 (d) 9882
33. 33.What is the smallest number you must take away from 350 so that it divides exactly by 4?
34. 34.What is the smallest number you must add to 366 so that it divides exactly by 12?
35. 35.How many factors does 47 have?
36. 36.What is the smallest number you must take away from 166 so that it divides exactly by 6?
37. 37.How many factors does 18 have?
38. 38.Which of these numbers divides exactly by 9? (a) 4433 (b) 4914 (c) 6271 (d) 2903
39. 39.How many factors does 27 have?
40. 40.Which of these numbers divides exactly by 9? (a) 5329 (b) 2806 (c) 3276 (d) 7282

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