Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 327 · 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.Which of these numbers divides exactly by 6? (a) 9082 (b) 6116 (c) 4423 (d) 9714
2. 2.How many factors does 71 have?
3. 3.Which of these numbers divides exactly by 6? (a) 7214 (b) 1189 (c) 9537 (d) 5796
4. 4.What is the smallest number you must add to 408 so that it divides exactly by 11?
5. 5.What is the smallest number you must take away from 978 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 615 so that it divides exactly by 9?
7. 7.How many factors does 34 have?
8. 8.Which of these numbers divides exactly by 11? (a) 7656 (b) 9651 (c) 9201 (d) 9400
9. 9.How many factors does 39 have?
10. 10.What is the smallest number you must take away from 638 so that it divides exactly by 8?
11. 11.What is the smallest number you must add to 532 so that it divides exactly by 11?
12. 12.Which of these numbers divides exactly by 6? (a) 9630 (b) 5284 (c) 6945 (d) 2585
13. 13.What is the smallest number you must add to 534 so that it divides exactly by 9?
14. 14.Which of these numbers divides exactly by 4? (a) 3853 (b) 9164 (c) 8421 (d) 5069
15. 15.How many factors does 30 have?
16. 16.What is the smallest number you must add to 515 so that it divides exactly by 4?
17. 17.How many factors does 75 have?
18. 18.What is the smallest number you must take away from 505 so that it divides exactly by 7?
19. 19.How many factors does 37 have?
20. 20.Which of these numbers divides exactly by 9? (a) 8038 (b) 5440 (c) 8008 (d) 6057
21. 21.What is the smallest number you must add to 385 so that it divides exactly by 13?
22. 22.How many factors does 29 have?
23. 23.Which of these numbers divides exactly by 9? (a) 5388 (b) 2243 (c) 1104 (d) 6615
24. 24.What is the smallest number you must take away from 646 so that it divides exactly by 11?
25. 25.How many factors does 14 have?
26. 26.What is the smallest number you must take away from 347 so that it divides exactly by 4?
27. 27.How many factors does 72 have?
28. 28.What is the smallest number you must add to 998 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 251 so that it divides exactly by 11?
30. 30.What is the smallest number you must take away from 157 so that it divides exactly by 3?
31. 31.What is the smallest number you must take away from 986 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 265 so that it divides exactly by 3?
33. 33.What is the smallest number you must add to 230 so that it divides exactly by 7?
34. 34.How many factors does 15 have?
35. 35.Which of these numbers divides exactly by 4? (a) 5773 (b) 6457 (c) 7178 (d) 3336
36. 36.What is the smallest number you must add to 962 so that it divides exactly by 7?
37. 37.How many factors does 21 have?
38. 38.What is the smallest number you must add to 303 so that it divides exactly by 6?
39. 39.How many factors does 23 have?
40. 40.Which of these numbers divides exactly by 6? (a) 5994 (b) 3808 (c) 4757 (d) 2213

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