Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 273 · 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 457 so that it divides exactly by 3?
2. 2.How many factors does 76 have?
3. 3.What is the smallest number you must add to 523 so that it divides exactly by 6?
4. 4.How many factors does 12 have?
5. 5.What is the smallest number you must add to 374 so that it divides exactly by 13?
6. 6.How many factors does 95 have?
7. 7.What is the smallest number you must take away from 326 so that it divides exactly by 7?
8. 8.How many factors does 81 have?
9. 9.Which of these numbers divides exactly by 4? (a) 2237 (b) 3489 (c) 7645 (d) 8908
10. 10.What is the smallest number you must add to 975 so that it divides exactly by 7?
11. 11.How many factors does 35 have?
12. 12.What is the smallest number you must add to 685 so that it divides exactly by 3?
13. 13.How many factors does 24 have?
14. 14.How many factors does 84 have?
15. 15.Which of these numbers divides exactly by 4? (a) 2252 (b) 5237 (c) 1455 (d) 4610
16. 16.Which of these numbers divides exactly by 6? (a) 7393 (b) 2076 (c) 3145 (d) 7364
17. 17.What is the smallest number you must add to 290 so that it divides exactly by 4?
18. 18.Which of these numbers divides exactly by 6? (a) 7267 (b) 1980 (c) 1079 (d) 1288
19. 19.What is the smallest number you must take away from 850 so that it divides exactly by 12?
20. 20.What is the smallest number you must take away from 292 so that it divides exactly by 9?
21. 21.What is the smallest number you must take away from 917 so that it divides exactly by 13?
22. 22.What is the smallest number you must add to 259 so that it divides exactly by 12?
23. 23.What is the smallest number you must add to 790 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 3? (a) 1786 (b) 7152 (c) 1717 (d) 5744
25. 25.What is the smallest number you must add to 618 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 6? (a) 6034 (b) 6649 (c) 2096 (d) 1440
27. 27.Which of these numbers divides exactly by 9? (a) 5168 (b) 3470 (c) 7345 (d) 3681
28. 28.How many factors does 45 have?
29. 29.What is the smallest number you must take away from 946 so that it divides exactly by 3?
30. 30.What is the smallest number you must take away from 317 so that it divides exactly by 3?
31. 31.What is the smallest number you must add to 526 so that it divides exactly by 8?
32. 32.What is the smallest number you must add to 436 so that it divides exactly by 9?
33. 33.What is the smallest number you must add to 746 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 290 so that it divides exactly by 6?
35. 35.How many factors does 99 have?
36. 36.What is the smallest number you must take away from 107 so that it divides exactly by 12?
37. 37.What is the smallest number you must take away from 263 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 410 so that it divides exactly by 8?
39. 39.Which of these numbers divides exactly by 3? (a) 1631 (b) 3396 (c) 7049 (d) 5843
40. 40.Which of these numbers divides exactly by 3? (a) 3046 (b) 6590 (c) 8947 (d) 8151

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