Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 262 · 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 6? (a) 4116 (b) 2780 (c) 2386 (d) 6824
2. 2.How many factors does 64 have?
3. 3.What is the smallest number you must add to 250 so that it divides exactly by 11?
4. 4.What is the smallest number you must add to 893 so that it divides exactly by 11?
5. 5.What is the smallest number you must take away from 512 so that it divides exactly by 11?
6. 6.How many factors does 31 have?
7. 7.What is the smallest number you must add to 816 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 398 so that it divides exactly by 6?
9. 9.What is the smallest number you must take away from 548 so that it divides exactly by 13?
10. 10.What is the smallest number you must take away from 561 so that it divides exactly by 7?
11. 11.What is the smallest number you must add to 709 so that it divides exactly by 4?
12. 12.How many factors does 39 have?
13. 13.How many factors does 53 have?
14. 14.Which of these numbers divides exactly by 4? (a) 1078 (b) 8604 (c) 2261 (d) 8257
15. 15.What is the smallest number you must take away from 811 so that it divides exactly by 13?
16. 16.What is the smallest number you must add to 969 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 3? (a) 7102 (b) 6489 (c) 2249 (d) 8792
18. 18.What is the smallest number you must add to 877 so that it divides exactly by 3?
19. 19.What is the smallest number you must add to 158 so that it divides exactly by 12?
20. 20.What is the smallest number you must add to 875 so that it divides exactly by 4?
21. 21.How many factors does 52 have?
22. 22.Which of these numbers divides exactly by 3? (a) 6602 (b) 3246 (c) 2561 (d) 6352
23. 23.How many factors does 98 have?
24. 24.What is the smallest number you must add to 562 so that it divides exactly by 6?
25. 25.What is the smallest number you must take away from 125 so that it divides exactly by 6?
26. 26.Which of these numbers divides exactly by 3? (a) 4219 (b) 3464 (c) 8645 (d) 1350
27. 27.Which of these numbers divides exactly by 11? (a) 3160 (b) 5833 (c) 6127 (d) 1206
28. 28.What is the smallest number you must take away from 679 so that it divides exactly by 9?
29. 29.Which of these numbers divides exactly by 9? (a) 7173 (b) 3608 (c) 5927 (d) 2414
30. 30.What is the smallest number you must add to 586 so that it divides exactly by 12?
31. 31.How many factors does 13 have?
32. 32.What is the smallest number you must take away from 721 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 4? (a) 6155 (b) 1389 (c) 4278 (d) 7068
34. 34.Which of these numbers divides exactly by 4? (a) 2013 (b) 5481 (c) 6831 (d) 1436
35. 35.How many factors does 80 have?
36. 36.Which of these numbers divides exactly by 8? (a) 1252 (b) 9928 (c) 4502 (d) 2829
37. 37.Which of these numbers divides exactly by 8? (a) 7856 (b) 9842 (c) 6869 (d) 1924
38. 38.Which of these numbers divides exactly by 3? (a) 9018 (b) 7397 (c) 8147 (d) 8195
39. 39.Which of these numbers divides exactly by 9? (a) 1214 (b) 7083 (c) 2123 (d) 4821
40. 40.Which of these numbers divides exactly by 8? (a) 2592 (b) 8723 (c) 4601 (d) 7215

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