Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 301 · 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) 2410 (b) 5359 (c) 3612 (d) 3906
2. 2.What is the smallest number you must take away from 313 so that it divides exactly by 12?
3. 3.What is the smallest number you must add to 651 so that it divides exactly by 13?
4. 4.What is the smallest number you must add to 157 so that it divides exactly by 4?
5. 5.How many factors does 54 have?
6. 6.How many factors does 27 have?
7. 7.What is the smallest number you must add to 314 so that it divides exactly by 8?
8. 8.How many factors does 52 have?
9. 9.How many factors does 93 have?
10. 10.What is the smallest number you must add to 398 so that it divides exactly by 8?
11. 11.Which of these numbers divides exactly by 3? (a) 6033 (b) 5062 (c) 3245 (d) 5152
12. 12.Which of these numbers divides exactly by 3? (a) 3841 (b) 6907 (c) 2635 (d) 5625
13. 13.How many factors does 43 have?
14. 14.How many factors does 72 have?
15. 15.Which of these numbers divides exactly by 8? (a) 1998 (b) 7103 (c) 9379 (d) 7112
16. 16.What is the smallest number you must add to 999 so that it divides exactly by 11?
17. 17.What is the smallest number you must take away from 802 so that it divides exactly by 6?
18. 18.What is the smallest number you must add to 355 so that it divides exactly by 3?
19. 19.How many factors does 36 have?
20. 20.What is the smallest number you must take away from 809 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 3? (a) 8468 (b) 1614 (c) 6763 (d) 7906
22. 22.What is the smallest number you must take away from 318 so that it divides exactly by 8?
23. 23.How many factors does 32 have?
24. 24.What is the smallest number you must take away from 461 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 358 so that it divides exactly by 13?
26. 26.What is the smallest number you must take away from 608 so that it divides exactly by 11?
27. 27.What is the smallest number you must take away from 989 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 822 so that it divides exactly by 12?
29. 29.What is the smallest number you must add to 534 so that it divides exactly by 7?
30. 30.What is the smallest number you must add to 692 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 3? (a) 4195 (b) 3411 (c) 5684 (d) 8888
32. 32.What is the smallest number you must take away from 973 so that it divides exactly by 4?
33. 33.How many factors does 84 have?
34. 34.Which of these numbers divides exactly by 6? (a) 6817 (b) 9051 (c) 3278 (d) 6930
35. 35.How many factors does 76 have?
36. 36.What is the smallest number you must take away from 132 so that it divides exactly by 7?
37. 37.Which of these numbers divides exactly by 6? (a) 4830 (b) 8257 (c) 4840 (d) 3319
38. 38.Which of these numbers divides exactly by 6? (a) 1429 (b) 1856 (c) 7796 (d) 2118
39. 39.Which of these numbers divides exactly by 6? (a) 2412 (b) 8543 (c) 2866 (d) 7277
40. 40.What is the smallest number you must add to 478 so that it divides exactly by 9?

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