Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 257 · 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.What is the smallest number you must add to 364 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 141 so that it divides exactly by 7?
3. 3.What is the smallest number you must take away from 762 so that it divides exactly by 13?
4. 4.Which of these numbers divides exactly by 9? (a) 2981 (b) 2034 (c) 7736 (d) 5341
5. 5.Which of these numbers divides exactly by 3? (a) 8000 (b) 3916 (c) 9597 (d) 9863
6. 6.How many factors does 41 have?
7. 7.Which of these numbers divides exactly by 6? (a) 2124 (b) 3788 (c) 5144 (d) 7977
8. 8.What is the smallest number you must add to 979 so that it divides exactly by 3?
9. 9.How many factors does 71 have?
10. 10.How many factors does 52 have?
11. 11.Which of these numbers divides exactly by 4? (a) 1584 (b) 1386 (c) 1787 (d) 5243
12. 12.Which of these numbers divides exactly by 3? (a) 4237 (b) 4114 (c) 9186 (d) 1685
13. 13.How many factors does 98 have?
14. 14.Which of these numbers divides exactly by 3? (a) 1103 (b) 1750 (c) 9842 (d) 7746
15. 15.How many factors does 83 have?
16. 16.What is the smallest number you must add to 387 so that it divides exactly by 4?
17. 17.What is the smallest number you must take away from 858 so that it divides exactly by 12?
18. 18.What is the smallest number you must add to 188 so that it divides exactly by 7?
19. 19.What is the smallest number you must add to 154 so that it divides exactly by 8?
20. 20.What is the smallest number you must take away from 790 so that it divides exactly by 8?
21. 21.How many factors does 87 have?
22. 22.What is the smallest number you must take away from 421 so that it divides exactly by 6?
23. 23.What is the smallest number you must take away from 783 so that it divides exactly by 11?
24. 24.What is the smallest number you must add to 645 so that it divides exactly by 8?
25. 25.What is the smallest number you must take away from 377 so that it divides exactly by 11?
26. 26.Which of these numbers divides exactly by 6? (a) 8594 (b) 8208 (c) 4691 (d) 9165
27. 27.How many factors does 23 have?
28. 28.How many factors does 100 have?
29. 29.What is the smallest number you must add to 775 so that it divides exactly by 9?
30. 30.What is the smallest number you must add to 524 so that it divides exactly by 7?
31. 31.How many factors does 16 have?
32. 32.What is the smallest number you must take away from 868 so that it divides exactly by 8?
33. 33.Which of these numbers divides exactly by 6? (a) 4710 (b) 6812 (c) 6284 (d) 3260
34. 34.Which of these numbers divides exactly by 8? (a) 5048 (b) 1033 (c) 8657 (d) 2314
35. 35.Which of these numbers divides exactly by 6? (a) 8688 (b) 5438 (c) 9645 (d) 4900
36. 36.What is the smallest number you must take away from 699 so that it divides exactly by 7?
37. 37.Which of these numbers divides exactly by 4? (a) 3507 (b) 1196 (c) 2419 (d) 4103
38. 38.What is the smallest number you must take away from 137 so that it divides exactly by 3?
39. 39.What is the smallest number you must take away from 538 so that it divides exactly by 6?
40. 40.What is the smallest number you must take away from 163 so that it divides exactly by 9?

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