Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 52 · 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 719 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 223 so that it divides exactly by 12?
3. 3.How many factors does 13 have?
4. 4.What is the smallest number you must take away from 723 so that it divides exactly by 13?
5. 5.Which of these numbers divides exactly by 6? (a) 9582 (b) 8823 (c) 7514 (d) 1895
6. 6.Which of these numbers divides exactly by 9? (a) 5334 (b) 6595 (c) 3709 (d) 1908
7. 7.What is the smallest number you must add to 153 so that it divides exactly by 8?
8. 8.How many factors does 100 have?
9. 9.What is the smallest number you must take away from 633 so that it divides exactly by 4?
10. 10.How many factors does 96 have?
11. 11.What is the smallest number you must add to 579 so that it divides exactly by 11?
12. 12.How many factors does 93 have?
13. 13.What is the smallest number you must take away from 957 so that it divides exactly by 13?
14. 14.What is the smallest number you must add to 123 so that it divides exactly by 9?
15. 15.Which of these numbers divides exactly by 8? (a) 4722 (b) 2882 (c) 2744 (d) 6404
16. 16.Which of these numbers divides exactly by 8? (a) 8840 (b) 6687 (c) 1327 (d) 5507
17. 17.Which of these numbers divides exactly by 6? (a) 3619 (b) 6881 (c) 9240 (d) 6715
18. 18.What is the smallest number you must add to 137 so that it divides exactly by 8?
19. 19.Which of these numbers divides exactly by 3? (a) 3395 (b) 1486 (c) 9826 (d) 2157
20. 20.How many factors does 56 have?
21. 21.Which of these numbers divides exactly by 9? (a) 6414 (b) 2478 (c) 1242 (d) 7585
22. 22.How many factors does 37 have?
23. 23.What is the smallest number you must add to 141 so that it divides exactly by 9?
24. 24.How many factors does 23 have?
25. 25.What is the smallest number you must take away from 878 so that it divides exactly by 4?
26. 26.What is the smallest number you must take away from 850 so that it divides exactly by 12?
27. 27.What is the smallest number you must take away from 798 so that it divides exactly by 8?
28. 28.How many factors does 52 have?
29. 29.How many factors does 47 have?
30. 30.What is the smallest number you must take away from 425 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 11? (a) 6118 (b) 5031 (c) 3822 (d) 1254
32. 32.What is the smallest number you must take away from 496 so that it divides exactly by 3?
33. 33.What is the smallest number you must add to 178 so that it divides exactly by 8?
34. 34.What is the smallest number you must take away from 646 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 3? (a) 1868 (b) 1364 (c) 2042 (d) 2301
36. 36.What is the smallest number you must take away from 382 so that it divides exactly by 6?
37. 37.How many factors does 98 have?
38. 38.How many factors does 80 have?
39. 39.How many factors does 60 have?
40. 40.What is the smallest number you must take away from 790 so that it divides exactly by 8?

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