Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 7 · 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 32 have?
2. 2.How many factors does 26 have?
3. 3.How many factors does 80 have?
4. 4.Which of these numbers divides exactly by 9? (a) 4302 (b) 9074 (c) 7404 (d) 1138
5. 5.How many factors does 96 have?
6. 6.How many factors does 54 have?
7. 7.What is the smallest number you must add to 705 so that it divides exactly by 6?
8. 8.How many factors does 63 have?
9. 9.Which of these numbers divides exactly by 3? (a) 1270 (b) 4678 (c) 9450 (d) 6368
10. 10.Which of these numbers divides exactly by 8? (a) 2681 (b) 5545 (c) 3774 (d) 5904
11. 11.What is the smallest number you must take away from 101 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 702 so that it divides exactly by 12?
13. 13.What is the smallest number you must take away from 861 so that it divides exactly by 9?
14. 14.What is the smallest number you must take away from 610 so that it divides exactly by 7?
15. 15.What is the smallest number you must take away from 838 so that it divides exactly by 7?
16. 16.What is the smallest number you must add to 272 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 11? (a) 1386 (b) 2368 (c) 1186 (d) 1867
18. 18.What is the smallest number you must add to 219 so that it divides exactly by 12?
19. 19.Which of these numbers divides exactly by 9? (a) 8831 (b) 8302 (c) 1818 (d) 9481
20. 20.Which of these numbers divides exactly by 3? (a) 6598 (b) 5055 (c) 4393 (d) 9884
21. 21.Which of these numbers divides exactly by 8? (a) 4685 (b) 7080 (c) 6254 (d) 2670
22. 22.What is the smallest number you must add to 143 so that it divides exactly by 12?
23. 23.Which of these numbers divides exactly by 9? (a) 2353 (b) 2011 (c) 2406 (d) 2529
24. 24.Which of these numbers divides exactly by 8? (a) 7744 (b) 9500 (c) 4402 (d) 6658
25. 25.Which of these numbers divides exactly by 3? (a) 4757 (b) 4411 (c) 7413 (d) 1466
26. 26.How many factors does 37 have?
27. 27.How many factors does 93 have?
28. 28.How many factors does 38 have?
29. 29.What is the smallest number you must add to 692 so that it divides exactly by 13?
30. 30.What is the smallest number you must add to 294 so that it divides exactly by 9?
31. 31.What is the smallest number you must take away from 105 so that it divides exactly by 8?
32. 32.Which of these numbers divides exactly by 8? (a) 9240 (b) 1061 (c) 7998 (d) 8465
33. 33.Which of these numbers divides exactly by 9? (a) 5292 (b) 2838 (c) 9830 (d) 4192
34. 34.What is the smallest number you must take away from 751 so that it divides exactly by 9?
35. 35.What is the smallest number you must add to 431 so that it divides exactly by 7?
36. 36.Which of these numbers divides exactly by 6? (a) 6254 (b) 5509 (c) 9720 (d) 1556
37. 37.Which of these numbers divides exactly by 6? (a) 8004 (b) 7825 (c) 1925 (d) 3554
38. 38.What is the smallest number you must add to 705 so that it divides exactly by 9?
39. 39.How many factors does 52 have?
40. 40.What is the smallest number you must take away from 777 so that it divides exactly by 9?

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