Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 336 · 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 99 have?
2. 2.What is the smallest number you must take away from 155 so that it divides exactly by 3?
3. 3.How many factors does 17 have?
4. 4.What is the smallest number you must add to 704 so that it divides exactly by 9?
5. 5.What is the smallest number you must take away from 511 so that it divides exactly by 3?
6. 6.What is the smallest number you must take away from 410 so that it divides exactly by 11?
7. 7.What is the smallest number you must add to 620 so that it divides exactly by 12?
8. 8.How many factors does 52 have?
9. 9.What is the smallest number you must take away from 912 so that it divides exactly by 13?
10. 10.What is the smallest number you must add to 175 so that it divides exactly by 3?
11. 11.How many factors does 72 have?
12. 12.Which of these numbers divides exactly by 9? (a) 4532 (b) 8967 (c) 7054 (d) 2079
13. 13.What is the smallest number you must take away from 385 so that it divides exactly by 3?
14. 14.What is the smallest number you must take away from 271 so that it divides exactly by 12?
15. 15.Which of these numbers divides exactly by 11? (a) 9778 (b) 1005 (c) 7405 (d) 5170
16. 16.What is the smallest number you must take away from 345 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 4? (a) 5566 (b) 5950 (c) 8832 (d) 3630
18. 18.Which of these numbers divides exactly by 9? (a) 8648 (b) 9936 (c) 8224 (d) 8754
19. 19.How many factors does 38 have?
20. 20.How many factors does 39 have?
21. 21.What is the smallest number you must take away from 172 so that it divides exactly by 8?
22. 22.What is the smallest number you must take away from 514 so that it divides exactly by 7?
23. 23.How many factors does 95 have?
24. 24.How many factors does 61 have?
25. 25.How many factors does 90 have?
26. 26.Which of these numbers divides exactly by 3? (a) 3193 (b) 8278 (c) 9231 (d) 7859
27. 27.Which of these numbers divides exactly by 6? (a) 2702 (b) 5796 (c) 1571 (d) 3607
28. 28.What is the smallest number you must add to 467 so that it divides exactly by 3?
29. 29.Which of these numbers divides exactly by 11? (a) 6593 (b) 4491 (c) 9729 (d) 5511
30. 30.How many factors does 40 have?
31. 31.What is the smallest number you must take away from 274 so that it divides exactly by 12?
32. 32.How many factors does 82 have?
33. 33.How many factors does 88 have?
34. 34.Which of these numbers divides exactly by 8? (a) 1369 (b) 4504 (c) 7845 (d) 8507
35. 35.Which of these numbers divides exactly by 11? (a) 1413 (b) 4763 (c) 1252 (d) 7584
36. 36.What is the smallest number you must add to 486 so that it divides exactly by 8?
37. 37.What is the smallest number you must add to 317 so that it divides exactly by 6?
38. 38.What is the smallest number you must add to 469 so that it divides exactly by 4?
39. 39.What is the smallest number you must take away from 319 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 846 so that it divides exactly by 7?

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