Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 329 · 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 63 have?
2. 2.What is the smallest number you must take away from 106 so that it divides exactly by 12?
3. 3.What is the smallest number you must add to 889 so that it divides exactly by 3?
4. 4.Which of these numbers divides exactly by 11? (a) 8922 (b) 2961 (c) 5771 (d) 5995
5. 5.Which of these numbers divides exactly by 3? (a) 1774 (b) 4307 (c) 1585 (d) 4254
6. 6.What is the smallest number you must take away from 233 so that it divides exactly by 3?
7. 7.What is the smallest number you must add to 941 so that it divides exactly by 6?
8. 8.What is the smallest number you must add to 437 so that it divides exactly by 8?
9. 9.What is the smallest number you must take away from 615 so that it divides exactly by 4?
10. 10.Which of these numbers divides exactly by 9? (a) 4822 (b) 6979 (c) 1123 (d) 5661
11. 11.How many factors does 99 have?
12. 12.Which of these numbers divides exactly by 6? (a) 7991 (b) 2259 (c) 2460 (d) 4819
13. 13.What is the smallest number you must add to 889 so that it divides exactly by 6?
14. 14.How many factors does 16 have?
15. 15.What is the smallest number you must add to 204 so that it divides exactly by 8?
16. 16.How many factors does 12 have?
17. 17.How many factors does 54 have?
18. 18.What is the smallest number you must add to 109 so that it divides exactly by 12?
19. 19.Which of these numbers divides exactly by 8? (a) 5741 (b) 8441 (c) 1800 (d) 9230
20. 20.What is the smallest number you must take away from 778 so that it divides exactly by 13?
21. 21.What is the smallest number you must add to 505 so that it divides exactly by 9?
22. 22.What is the smallest number you must add to 112 so that it divides exactly by 3?
23. 23.How many factors does 81 have?
24. 24.What is the smallest number you must add to 905 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 593 so that it divides exactly by 8?
26. 26.How many factors does 89 have?
27. 27.How many factors does 77 have?
28. 28.Which of these numbers divides exactly by 4? (a) 2220 (b) 6931 (c) 9771 (d) 6917
29. 29.What is the smallest number you must take away from 916 so that it divides exactly by 11?
30. 30.How many factors does 46 have?
31. 31.Which of these numbers divides exactly by 6? (a) 4558 (b) 4809 (c) 9888 (d) 2367
32. 32.What is the smallest number you must take away from 553 so that it divides exactly by 12?
33. 33.How many factors does 83 have?
34. 34.Which of these numbers divides exactly by 4? (a) 9184 (b) 8853 (c) 3043 (d) 3921
35. 35.What is the smallest number you must take away from 167 so that it divides exactly by 11?
36. 36.What is the smallest number you must add to 298 so that it divides exactly by 9?
37. 37.Which of these numbers divides exactly by 11? (a) 1150 (b) 7128 (c) 7987 (d) 4693
38. 38.Which of these numbers divides exactly by 3? (a) 1873 (b) 9079 (c) 5486 (d) 2856
39. 39.What is the smallest number you must add to 536 so that it divides exactly by 12?
40. 40.Which of these numbers divides exactly by 9? (a) 1248 (b) 1756 (c) 2457 (d) 4874

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