Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 90 · 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 take away from 863 so that it divides exactly by 12?
2. 2.Which of these numbers divides exactly by 11? (a) 9943 (b) 3749 (c) 6336 (d) 3954
3. 3.What is the smallest number you must take away from 240 so that it divides exactly by 11?
4. 4.What is the smallest number you must add to 128 so that it divides exactly by 9?
5. 5.How many factors does 27 have?
6. 6.What is the smallest number you must take away from 335 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 879 so that it divides exactly by 13?
8. 8.What is the smallest number you must add to 252 so that it divides exactly by 11?
9. 9.Which of these numbers divides exactly by 4? (a) 2759 (b) 2745 (c) 7742 (d) 7728
10. 10.How many factors does 71 have?
11. 11.What is the smallest number you must add to 742 so that it divides exactly by 8?
12. 12.Which of these numbers divides exactly by 3? (a) 2714 (b) 1647 (c) 8785 (d) 5411
13. 13.What is the smallest number you must add to 412 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 756 so that it divides exactly by 11?
15. 15.How many factors does 30 have?
16. 16.Which of these numbers divides exactly by 6? (a) 4005 (b) 8724 (c) 8576 (d) 7307
17. 17.What is the smallest number you must take away from 522 so that it divides exactly by 13?
18. 18.Which of these numbers divides exactly by 9? (a) 5493 (b) 7126 (c) 1819 (d) 5040
19. 19.What is the smallest number you must add to 343 so that it divides exactly by 12?
20. 20.What is the smallest number you must add to 419 so that it divides exactly by 7?
21. 21.Which of these numbers divides exactly by 8? (a) 3400 (b) 5642 (c) 1671 (d) 1354
22. 22.What is the smallest number you must add to 238 so that it divides exactly by 3?
23. 23.How many factors does 20 have?
24. 24.What is the smallest number you must add to 552 so that it divides exactly by 11?
25. 25.What is the smallest number you must take away from 102 so that it divides exactly by 13?
26. 26.What is the smallest number you must add to 719 so that it divides exactly by 11?
27. 27.What is the smallest number you must add to 295 so that it divides exactly by 9?
28. 28.How many factors does 26 have?
29. 29.What is the smallest number you must take away from 497 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 9? (a) 3247 (b) 8840 (c) 2400 (d) 4113
31. 31.How many factors does 22 have?
32. 32.What is the smallest number you must take away from 975 so that it divides exactly by 12?
33. 33.Which of these numbers divides exactly by 8? (a) 8734 (b) 3560 (c) 8229 (d) 9626
34. 34.What is the smallest number you must add to 807 so that it divides exactly by 13?
35. 35.What is the smallest number you must add to 643 so that it divides exactly by 7?
36. 36.How many factors does 53 have?
37. 37.Which of these numbers divides exactly by 11? (a) 4927 (b) 5830 (c) 5232 (d) 5013
38. 38.What is the smallest number you must take away from 823 so that it divides exactly by 3?
39. 39.Which of these numbers divides exactly by 4? (a) 3075 (b) 3391 (c) 6744 (d) 5946
40. 40.How many factors does 28 have?

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