Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 244 · 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 782 so that it divides exactly by 6?
2. 2.Which of these numbers divides exactly by 9? (a) 6077 (b) 6471 (c) 3451 (d) 3877
3. 3.Which of these numbers divides exactly by 8? (a) 5052 (b) 4326 (c) 8047 (d) 7560
4. 4.Which of these numbers divides exactly by 11? (a) 2565 (b) 2068 (c) 7193 (d) 2020
5. 5.How many factors does 77 have?
6. 6.Which of these numbers divides exactly by 3? (a) 2269 (b) 4299 (c) 9229 (d) 7832
7. 7.How many factors does 79 have?
8. 8.How many factors does 35 have?
9. 9.How many factors does 47 have?
10. 10.Which of these numbers divides exactly by 11? (a) 1956 (b) 7857 (c) 9580 (d) 4631
11. 11.What is the smallest number you must add to 915 so that it divides exactly by 13?
12. 12.What is the smallest number you must take away from 570 so that it divides exactly by 8?
13. 13.How many factors does 60 have?
14. 14.How many factors does 78 have?
15. 15.What is the smallest number you must add to 172 so that it divides exactly by 7?
16. 16.What is the smallest number you must take away from 244 so that it divides exactly by 9?
17. 17.Which of these numbers divides exactly by 4? (a) 1530 (b) 2645 (c) 5650 (d) 1288
18. 18.What is the smallest number you must take away from 164 so that it divides exactly by 13?
19. 19.What is the smallest number you must add to 872 so that it divides exactly by 9?
20. 20.How many factors does 67 have?
21. 21.What is the smallest number you must take away from 244 so that it divides exactly by 8?
22. 22.How many factors does 38 have?
23. 23.What is the smallest number you must add to 262 so that it divides exactly by 13?
24. 24.What is the smallest number you must add to 436 so that it divides exactly by 7?
25. 25.What is the smallest number you must take away from 198 so that it divides exactly by 13?
26. 26.Which of these numbers divides exactly by 3? (a) 2204 (b) 4764 (c) 8228 (d) 7873
27. 27.What is the smallest number you must take away from 332 so that it divides exactly by 3?
28. 28.How many factors does 88 have?
29. 29.What is the smallest number you must add to 729 so that it divides exactly by 13?
30. 30.What is the smallest number you must add to 669 so that it divides exactly by 6?
31. 31.What is the smallest number you must add to 365 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 8? (a) 7115 (b) 8869 (c) 4867 (d) 6416
33. 33.Which of these numbers divides exactly by 3? (a) 4263 (b) 5809 (c) 1636 (d) 1414
34. 34.What is the smallest number you must add to 964 so that it divides exactly by 8?
35. 35.What is the smallest number you must take away from 934 so that it divides exactly by 11?
36. 36.What is the smallest number you must add to 755 so that it divides exactly by 9?
37. 37.How many factors does 44 have?
38. 38.What is the smallest number you must add to 341 so that it divides exactly by 12?
39. 39.How many factors does 26 have?
40. 40.What is the smallest number you must add to 727 so that it divides exactly by 13?

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