Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 61 · 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 165 so that it divides exactly by 6?
2. 2.What is the smallest number you must add to 299 so that it divides exactly by 12?
3. 3.What is the smallest number you must take away from 595 so that it divides exactly by 11?
4. 4.Which of these numbers divides exactly by 4? (a) 8987 (b) 9144 (c) 2697 (d) 5829
5. 5.What is the smallest number you must add to 476 so that it divides exactly by 8?
6. 6.What is the smallest number you must take away from 246 so that it divides exactly by 12?
7. 7.How many factors does 91 have?
8. 8.What is the smallest number you must add to 297 so that it divides exactly by 4?
9. 9.What is the smallest number you must add to 229 so that it divides exactly by 3?
10. 10.Which of these numbers divides exactly by 6? (a) 3279 (b) 3870 (c) 4660 (d) 5317
11. 11.What is the smallest number you must take away from 555 so that it divides exactly by 8?
12. 12.What is the smallest number you must take away from 265 so that it divides exactly by 4?
13. 13.What is the smallest number you must take away from 533 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 367 so that it divides exactly by 11?
15. 15.How many factors does 71 have?
16. 16.What is the smallest number you must add to 825 so that it divides exactly by 7?
17. 17.What is the smallest number you must add to 801 so that it divides exactly by 8?
18. 18.What is the smallest number you must take away from 358 so that it divides exactly by 9?
19. 19.What is the smallest number you must take away from 476 so that it divides exactly by 3?
20. 20.What is the smallest number you must add to 608 so that it divides exactly by 3?
21. 21.How many factors does 89 have?
22. 22.What is the smallest number you must take away from 626 so that it divides exactly by 3?
23. 23.How many factors does 43 have?
24. 24.How many factors does 26 have?
25. 25.What is the smallest number you must take away from 263 so that it divides exactly by 6?
26. 26.Which of these numbers divides exactly by 6? (a) 1651 (b) 5238 (c) 3249 (d) 5092
27. 27.What is the smallest number you must take away from 514 so that it divides exactly by 7?
28. 28.How many factors does 84 have?
29. 29.What is the smallest number you must take away from 310 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 314 so that it divides exactly by 8?
31. 31.Which of these numbers divides exactly by 3? (a) 7592 (b) 4943 (c) 7803 (d) 5674
32. 32.Which of these numbers divides exactly by 6? (a) 4838 (b) 3268 (c) 1068 (d) 3045
33. 33.What is the smallest number you must take away from 905 so that it divides exactly by 9?
34. 34.What is the smallest number you must take away from 659 so that it divides exactly by 9?
35. 35.How many factors does 40 have?
36. 36.What is the smallest number you must take away from 856 so that it divides exactly by 11?
37. 37.How many factors does 77 have?
38. 38.How many factors does 95 have?
39. 39.How many factors does 29 have?
40. 40.What is the smallest number you must add to 735 so that it divides exactly by 6?

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