Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 219 · 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 91 have?
2. 2.What is the smallest number you must add to 461 so that it divides exactly by 9?
3. 3.What is the smallest number you must take away from 694 so that it divides exactly by 9?
4. 4.What is the smallest number you must take away from 386 so that it divides exactly by 7?
5. 5.How many factors does 74 have?
6. 6.How many factors does 69 have?
7. 7.What is the smallest number you must take away from 262 so that it divides exactly by 13?
8. 8.How many factors does 50 have?
9. 9.What is the smallest number you must take away from 101 so that it divides exactly by 8?
10. 10.What is the smallest number you must take away from 184 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 106 so that it divides exactly by 4?
12. 12.What is the smallest number you must take away from 460 so that it divides exactly by 12?
13. 13.What is the smallest number you must take away from 250 so that it divides exactly by 4?
14. 14.Which of these numbers divides exactly by 3? (a) 1544 (b) 6088 (c) 1514 (d) 2400
15. 15.What is the smallest number you must take away from 394 so that it divides exactly by 7?
16. 16.Which of these numbers divides exactly by 11? (a) 4268 (b) 4154 (c) 7890 (d) 6348
17. 17.Which of these numbers divides exactly by 11? (a) 1705 (b) 7228 (c) 3040 (d) 4890
18. 18.What is the smallest number you must take away from 842 so that it divides exactly by 4?
19. 19.What is the smallest number you must add to 201 so that it divides exactly by 8?
20. 20.How many factors does 35 have?
21. 21.How many factors does 33 have?
22. 22.How many factors does 43 have?
23. 23.How many factors does 40 have?
24. 24.How many factors does 21 have?
25. 25.What is the smallest number you must take away from 139 so that it divides exactly by 4?
26. 26.What is the smallest number you must take away from 586 so that it divides exactly by 8?
27. 27.What is the smallest number you must add to 162 so that it divides exactly by 13?
28. 28.How many factors does 96 have?
29. 29.Which of these numbers divides exactly by 4? (a) 8419 (b) 5853 (c) 5734 (d) 4252
30. 30.What is the smallest number you must take away from 451 so that it divides exactly by 6?
31. 31.What is the smallest number you must take away from 754 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 382 so that it divides exactly by 6?
33. 33.Which of these numbers divides exactly by 4? (a) 4636 (b) 2981 (c) 7637 (d) 6285
34. 34.What is the smallest number you must take away from 705 so that it divides exactly by 8?
35. 35.How many factors does 44 have?
36. 36.What is the smallest number you must add to 485 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 581 so that it divides exactly by 11?
38. 38.Which of these numbers divides exactly by 11? (a) 3999 (b) 9940 (c) 8220 (d) 1782
39. 39.What is the smallest number you must add to 757 so that it divides exactly by 11?
40. 40.Which of these numbers divides exactly by 11? (a) 2944 (b) 5544 (c) 3211 (d) 6114

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