Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 121 · 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 3? (a) 2726 (b) 2166 (c) 2890 (d) 5542
2. 2.How many factors does 44 have?
3. 3.What is the smallest number you must take away from 218 so that it divides exactly by 12?
4. 4.What is the smallest number you must add to 164 so that it divides exactly by 9?
5. 5.Which of these numbers divides exactly by 3? (a) 1835 (b) 8415 (c) 3592 (d) 3170
6. 6.What is the smallest number you must take away from 289 so that it divides exactly by 13?
7. 7.How many factors does 37 have?
8. 8.What is the smallest number you must take away from 375 so that it divides exactly by 8?
9. 9.What is the smallest number you must add to 771 so that it divides exactly by 6?
10. 10.How many factors does 28 have?
11. 11.What is the smallest number you must add to 280 so that it divides exactly by 11?
12. 12.What is the smallest number you must add to 347 so that it divides exactly by 9?
13. 13.What is the smallest number you must take away from 574 so that it divides exactly by 13?
14. 14.How many factors does 67 have?
15. 15.What is the smallest number you must take away from 379 so that it divides exactly by 8?
16. 16.Which of these numbers divides exactly by 11? (a) 6418 (b) 7469 (c) 8462 (d) 9841
17. 17.What is the smallest number you must add to 688 so that it divides exactly by 7?
18. 18.What is the smallest number you must take away from 644 so that it divides exactly by 8?
19. 19.What is the smallest number you must add to 649 so that it divides exactly by 13?
20. 20.What is the smallest number you must take away from 256 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 4? (a) 3816 (b) 1517 (c) 8025 (d) 4069
22. 22.What is the smallest number you must take away from 395 so that it divides exactly by 7?
23. 23.What is the smallest number you must add to 436 so that it divides exactly by 8?
24. 24.How many factors does 48 have?
25. 25.What is the smallest number you must add to 905 so that it divides exactly by 8?
26. 26.What is the smallest number you must add to 569 so that it divides exactly by 7?
27. 27.What is the smallest number you must take away from 481 so that it divides exactly by 6?
28. 28.What is the smallest number you must take away from 711 so that it divides exactly by 13?
29. 29.How many factors does 38 have?
30. 30.What is the smallest number you must take away from 646 so that it divides exactly by 12?
31. 31.What is the smallest number you must add to 795 so that it divides exactly by 7?
32. 32.Which of these numbers divides exactly by 8? (a) 6357 (b) 6694 (c) 2510 (d) 7672
33. 33.Which of these numbers divides exactly by 3? (a) 8682 (b) 6047 (c) 1175 (d) 3604
34. 34.How many factors does 96 have?
35. 35.What is the smallest number you must add to 557 so that it divides exactly by 8?
36. 36.What is the smallest number you must add to 410 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 821 so that it divides exactly by 6?
38. 38.Which of these numbers divides exactly by 11? (a) 9064 (b) 4699 (c) 4033 (d) 6240
39. 39.Which of these numbers divides exactly by 3? (a) 8573 (b) 7745 (c) 4738 (d) 6378
40. 40.What is the smallest number you must take away from 328 so that it divides exactly by 13?

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