Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 13 · 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 70 have?
2. 2.What is the smallest number you must add to 287 so that it divides exactly by 8?
3. 3.Which of these numbers divides exactly by 3? (a) 3205 (b) 7909 (c) 7838 (d) 6972
4. 4.Which of these numbers divides exactly by 11? (a) 3561 (b) 1808 (c) 6939 (d) 1881
5. 5.How many factors does 95 have?
6. 6.How many factors does 17 have?
7. 7.Which of these numbers divides exactly by 4? (a) 9101 (b) 6720 (c) 4618 (d) 3723
8. 8.Which of these numbers divides exactly by 8? (a) 8276 (b) 5464 (c) 4273 (d) 5674
9. 9.Which of these numbers divides exactly by 9? (a) 6744 (b) 6025 (c) 9780 (d) 6732
10. 10.What is the smallest number you must take away from 311 so that it divides exactly by 3?
11. 11.What is the smallest number you must take away from 935 so that it divides exactly by 9?
12. 12.How many factors does 98 have?
13. 13.How many factors does 41 have?
14. 14.What is the smallest number you must take away from 895 so that it divides exactly by 4?
15. 15.What is the smallest number you must take away from 626 so that it divides exactly by 4?
16. 16.What is the smallest number you must add to 970 so that it divides exactly by 4?
17. 17.Which of these numbers divides exactly by 11? (a) 3181 (b) 4446 (c) 3570 (d) 4587
18. 18.What is the smallest number you must add to 440 so that it divides exactly by 9?
19. 19.What is the smallest number you must add to 313 so that it divides exactly by 13?
20. 20.What is the smallest number you must add to 333 so that it divides exactly by 8?
21. 21.What is the smallest number you must add to 113 so that it divides exactly by 13?
22. 22.Which of these numbers divides exactly by 9? (a) 9664 (b) 3130 (c) 1188 (d) 1571
23. 23.What is the smallest number you must add to 232 so that it divides exactly by 3?
24. 24.What is the smallest number you must take away from 359 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 103 so that it divides exactly by 7?
26. 26.How many factors does 97 have?
27. 27.What is the smallest number you must take away from 484 so that it divides exactly by 3?
28. 28.Which of these numbers divides exactly by 6? (a) 6074 (b) 2634 (c) 2174 (d) 1769
29. 29.What is the smallest number you must take away from 714 so that it divides exactly by 9?
30. 30.Which of these numbers divides exactly by 4? (a) 7779 (b) 1421 (c) 1836 (d) 5337
31. 31.Which of these numbers divides exactly by 9? (a) 4405 (b) 1448 (c) 7487 (d) 9198
32. 32.What is the smallest number you must add to 427 so that it divides exactly by 6?
33. 33.How many factors does 60 have?
34. 34.What is the smallest number you must add to 554 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 815 so that it divides exactly by 13?
36. 36.What is the smallest number you must add to 111 so that it divides exactly by 6?
37. 37.How many factors does 78 have?
38. 38.How many factors does 72 have?
39. 39.What is the smallest number you must take away from 163 so that it divides exactly by 8?
40. 40.How many factors does 42 have?

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