Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 173 · 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 29 have?
2. 2.What is the smallest number you must take away from 202 so that it divides exactly by 12?
3. 3.Which of these numbers divides exactly by 3? (a) 8167 (b) 2941 (c) 9528 (d) 4375
4. 4.What is the smallest number you must add to 129 so that it divides exactly by 9?
5. 5.What is the smallest number you must take away from 611 so that it divides exactly by 12?
6. 6.What is the smallest number you must take away from 240 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 4? (a) 4050 (b) 1570 (c) 1142 (d) 4928
8. 8.What is the smallest number you must take away from 719 so that it divides exactly by 4?
9. 9.How many factors does 49 have?
10. 10.What is the smallest number you must take away from 963 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 140 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 8? (a) 3165 (b) 2302 (c) 7840 (d) 4755
13. 13.What is the smallest number you must add to 269 so that it divides exactly by 11?
14. 14.Which of these numbers divides exactly by 4? (a) 2248 (b) 4631 (c) 7850 (d) 4902
15. 15.Which of these numbers divides exactly by 9? (a) 7955 (b) 9353 (c) 6201 (d) 9122
16. 16.Which of these numbers divides exactly by 3? (a) 7103 (b) 9166 (c) 3783 (d) 2921
17. 17.How many factors does 69 have?
18. 18.What is the smallest number you must add to 918 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 426 so that it divides exactly by 4?
20. 20.Which of these numbers divides exactly by 8? (a) 5131 (b) 6592 (c) 6919 (d) 9844
21. 21.What is the smallest number you must add to 363 so that it divides exactly by 9?
22. 22.How many factors does 37 have?
23. 23.How many factors does 14 have?
24. 24.What is the smallest number you must take away from 812 so that it divides exactly by 11?
25. 25.What is the smallest number you must take away from 551 so that it divides exactly by 7?
26. 26.What is the smallest number you must take away from 589 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 758 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 873 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 316 so that it divides exactly by 12?
30. 30.What is the smallest number you must add to 385 so that it divides exactly by 6?
31. 31.Which of these numbers divides exactly by 3? (a) 2687 (b) 4999 (c) 4239 (d) 9700
32. 32.Which of these numbers divides exactly by 3? (a) 8248 (b) 2641 (c) 6964 (d) 4245
33. 33.How many factors does 93 have?
34. 34.Which of these numbers divides exactly by 3? (a) 9417 (b) 5020 (c) 2551 (d) 7232
35. 35.How many factors does 86 have?
36. 36.Which of these numbers divides exactly by 4? (a) 6917 (b) 2637 (c) 9408 (d) 1443
37. 37.What is the smallest number you must add to 994 so that it divides exactly by 9?
38. 38.How many factors does 16 have?
39. 39.What is the smallest number you must take away from 489 so that it divides exactly by 12?
40. 40.How many factors does 27 have?

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