Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 110 · 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 60 have?
2. 2.What is the smallest number you must take away from 922 so that it divides exactly by 12?
3. 3.What is the smallest number you must add to 348 so that it divides exactly by 8?
4. 4.What is the smallest number you must add to 391 so that it divides exactly by 6?
5. 5.Which of these numbers divides exactly by 9? (a) 6455 (b) 1866 (c) 3962 (d) 1818
6. 6.What is the smallest number you must take away from 244 so that it divides exactly by 9?
7. 7.How many factors does 85 have?
8. 8.Which of these numbers divides exactly by 3? (a) 4753 (b) 8905 (c) 5120 (d) 1149
9. 9.How many factors does 31 have?
10. 10.What is the smallest number you must add to 797 so that it divides exactly by 3?
11. 11.How many factors does 87 have?
12. 12.What is the smallest number you must take away from 514 so that it divides exactly by 4?
13. 13.What is the smallest number you must add to 321 so that it divides exactly by 11?
14. 14.Which of these numbers divides exactly by 6? (a) 7960 (b) 9968 (c) 9690 (d) 6749
15. 15.How many factors does 92 have?
16. 16.What is the smallest number you must add to 177 so that it divides exactly by 4?
17. 17.What is the smallest number you must take away from 986 so that it divides exactly by 11?
18. 18.What is the smallest number you must add to 476 so that it divides exactly by 8?
19. 19.What is the smallest number you must add to 682 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 677 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 661 so that it divides exactly by 12?
22. 22.How many factors does 16 have?
23. 23.What is the smallest number you must take away from 728 so that it divides exactly by 3?
24. 24.What is the smallest number you must take away from 457 so that it divides exactly by 9?
25. 25.How many factors does 29 have?
26. 26.What is the smallest number you must add to 184 so that it divides exactly by 3?
27. 27.How many factors does 93 have?
28. 28.What is the smallest number you must take away from 464 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 363 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 4? (a) 1209 (b) 6757 (c) 2684 (d) 3607
31. 31.What is the smallest number you must add to 426 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 8? (a) 3819 (b) 6727 (c) 5744 (d) 5762
33. 33.What is the smallest number you must add to 606 so that it divides exactly by 12?
34. 34.How many factors does 59 have?
35. 35.Which of these numbers divides exactly by 9? (a) 9151 (b) 1241 (c) 1369 (d) 1575
36. 36.How many factors does 50 have?
37. 37.Which of these numbers divides exactly by 8? (a) 1599 (b) 9690 (c) 6300 (d) 7080
38. 38.How many factors does 47 have?
39. 39.Which of these numbers divides exactly by 11? (a) 5702 (b) 3180 (c) 3685 (d) 5686
40. 40.What is the smallest number you must take away from 182 so that it divides exactly by 8?

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