Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 141 · 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 903 so that it divides exactly by 11?
2. 2.What is the smallest number you must take away from 969 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 432 so that it divides exactly by 13?
4. 4.How many factors does 67 have?
5. 5.What is the smallest number you must add to 501 so that it divides exactly by 6?
6. 6.Which of these numbers divides exactly by 11? (a) 6024 (b) 2092 (c) 5049 (d) 8234
7. 7.How many factors does 35 have?
8. 8.How many factors does 57 have?
9. 9.Which of these numbers divides exactly by 9? (a) 6390 (b) 1075 (c) 6391 (d) 2296
10. 10.Which of these numbers divides exactly by 4? (a) 6772 (b) 1793 (c) 7501 (d) 8854
11. 11.Which of these numbers divides exactly by 3? (a) 6654 (b) 1366 (c) 3439 (d) 5326
12. 12.What is the smallest number you must add to 197 so that it divides exactly by 7?
13. 13.What is the smallest number you must add to 344 so that it divides exactly by 7?
14. 14.How many factors does 43 have?
15. 15.What is the smallest number you must take away from 710 so that it divides exactly by 6?
16. 16.What is the smallest number you must take away from 424 so that it divides exactly by 3?
17. 17.What is the smallest number you must take away from 289 so that it divides exactly by 9?
18. 18.What is the smallest number you must add to 170 so that it divides exactly by 6?
19. 19.How many factors does 70 have?
20. 20.What is the smallest number you must take away from 737 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 375 so that it divides exactly by 13?
22. 22.Which of these numbers divides exactly by 11? (a) 1364 (b) 6362 (c) 7178 (d) 2784
23. 23.Which of these numbers divides exactly by 11? (a) 1282 (b) 5375 (c) 1902 (d) 9108
24. 24.What is the smallest number you must take away from 619 so that it divides exactly by 8?
25. 25.What is the smallest number you must take away from 202 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 8? (a) 9208 (b) 5189 (c) 2012 (d) 6023
27. 27.How many factors does 42 have?
28. 28.How many factors does 31 have?
29. 29.Which of these numbers divides exactly by 8? (a) 6858 (b) 6168 (c) 8738 (d) 4590
30. 30.How many factors does 65 have?
31. 31.Which of these numbers divides exactly by 3? (a) 8879 (b) 6407 (c) 9510 (d) 3649
32. 32.Which of these numbers divides exactly by 4? (a) 1378 (b) 9444 (c) 6923 (d) 1183
33. 33.How many factors does 30 have?
34. 34.Which of these numbers divides exactly by 6? (a) 9482 (b) 1488 (c) 6907 (d) 8030
35. 35.What is the smallest number you must take away from 397 so that it divides exactly by 8?
36. 36.How many factors does 89 have?
37. 37.What is the smallest number you must take away from 434 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 464 so that it divides exactly by 3?
39. 39.What is the smallest number you must take away from 968 so that it divides exactly by 6?
40. 40.Which of these numbers divides exactly by 8? (a) 5454 (b) 1341 (c) 6920 (d) 1833

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