Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 268 · 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 859 so that it divides exactly by 3?
2. 2.Which of these numbers divides exactly by 3? (a) 3773 (b) 9935 (c) 7098 (d) 7234
3. 3.What is the smallest number you must take away from 966 so that it divides exactly by 9?
4. 4.What is the smallest number you must add to 957 so that it divides exactly by 13?
5. 5.How many factors does 80 have?
6. 6.What is the smallest number you must add to 535 so that it divides exactly by 4?
7. 7.How many factors does 15 have?
8. 8.What is the smallest number you must take away from 742 so that it divides exactly by 6?
9. 9.Which of these numbers divides exactly by 8? (a) 2988 (b) 6040 (c) 3629 (d) 9687
10. 10.What is the smallest number you must take away from 257 so that it divides exactly by 7?
11. 11.Which of these numbers divides exactly by 8? (a) 8173 (b) 1699 (c) 1800 (d) 3261
12. 12.What is the smallest number you must take away from 283 so that it divides exactly by 11?
13. 13.What is the smallest number you must add to 188 so that it divides exactly by 3?
14. 14.How many factors does 96 have?
15. 15.Which of these numbers divides exactly by 3? (a) 2360 (b) 1851 (c) 1543 (d) 9661
16. 16.What is the smallest number you must take away from 574 so that it divides exactly by 8?
17. 17.What is the smallest number you must take away from 107 so that it divides exactly by 7?
18. 18.What is the smallest number you must add to 445 so that it divides exactly by 8?
19. 19.How many factors does 64 have?
20. 20.How many factors does 23 have?
21. 21.What is the smallest number you must add to 347 so that it divides exactly by 4?
22. 22.How many factors does 87 have?
23. 23.Which of these numbers divides exactly by 11? (a) 3166 (b) 2400 (c) 3010 (d) 1386
24. 24.How many factors does 95 have?
25. 25.Which of these numbers divides exactly by 6? (a) 9034 (b) 5442 (c) 8386 (d) 2837
26. 26.Which of these numbers divides exactly by 4? (a) 5793 (b) 8714 (c) 4916 (d) 4473
27. 27.What is the smallest number you must take away from 815 so that it divides exactly by 13?
28. 28.What is the smallest number you must add to 197 so that it divides exactly by 13?
29. 29.What is the smallest number you must add to 207 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 464 so that it divides exactly by 3?
31. 31.What is the smallest number you must take away from 725 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 6? (a) 3136 (b) 2993 (c) 6533 (d) 3504
33. 33.What is the smallest number you must add to 162 so that it divides exactly by 13?
34. 34.Which of these numbers divides exactly by 6? (a) 5512 (b) 2785 (c) 6966 (d) 2020
35. 35.What is the smallest number you must add to 912 so that it divides exactly by 7?
36. 36.How many factors does 19 have?
37. 37.What is the smallest number you must take away from 877 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 707 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 3? (a) 5079 (b) 1570 (c) 2291 (d) 3157
40. 40.How many factors does 69 have?

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