Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 131 · 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 697 so that it divides exactly by 4?
2. 2.How many factors does 31 have?
3. 3.How many factors does 17 have?
4. 4.Which of these numbers divides exactly by 11? (a) 4125 (b) 6219 (c) 3241 (d) 1506
5. 5.Which of these numbers divides exactly by 4? (a) 1045 (b) 4484 (c) 2797 (d) 7481
6. 6.Which of these numbers divides exactly by 11? (a) 5003 (b) 9178 (c) 4951 (d) 7502
7. 7.How many factors does 79 have?
8. 8.Which of these numbers divides exactly by 11? (a) 4547 (b) 6421 (c) 6550 (d) 4708
9. 9.What is the smallest number you must add to 487 so that it divides exactly by 3?
10. 10.What is the smallest number you must add to 218 so that it divides exactly by 12?
11. 11.What is the smallest number you must add to 295 so that it divides exactly by 9?
12. 12.Which of these numbers divides exactly by 4? (a) 2633 (b) 1952 (c) 2966 (d) 2250
13. 13.What is the smallest number you must add to 887 so that it divides exactly by 7?
14. 14.What is the smallest number you must add to 917 so that it divides exactly by 6?
15. 15.How many factors does 64 have?
16. 16.Which of these numbers divides exactly by 8? (a) 8419 (b) 9880 (c) 4397 (d) 9225
17. 17.What is the smallest number you must take away from 335 so that it divides exactly by 9?
18. 18.What is the smallest number you must take away from 161 so that it divides exactly by 6?
19. 19.How many factors does 14 have?
20. 20.What is the smallest number you must take away from 378 so that it divides exactly by 13?
21. 21.Which of these numbers divides exactly by 3? (a) 2219 (b) 6237 (c) 7957 (d) 5083
22. 22.What is the smallest number you must add to 479 so that it divides exactly by 13?
23. 23.Which of these numbers divides exactly by 8? (a) 1448 (b) 2206 (c) 7071 (d) 2492
24. 24.Which of these numbers divides exactly by 6? (a) 4177 (b) 4004 (c) 4417 (d) 9240
25. 25.What is the smallest number you must take away from 500 so that it divides exactly by 9?
26. 26.Which of these numbers divides exactly by 11? (a) 5484 (b) 7634 (c) 1042 (d) 7611
27. 27.Which of these numbers divides exactly by 11? (a) 4704 (b) 7698 (c) 1193 (d) 8217
28. 28.What is the smallest number you must take away from 661 so that it divides exactly by 4?
29. 29.How many factors does 16 have?
30. 30.What is the smallest number you must take away from 160 so that it divides exactly by 3?
31. 31.What is the smallest number you must take away from 593 so that it divides exactly by 9?
32. 32.How many factors does 42 have?
33. 33.How many factors does 62 have?
34. 34.How many factors does 37 have?
35. 35.What is the smallest number you must take away from 340 so that it divides exactly by 13?
36. 36.How many factors does 40 have?
37. 37.Which of these numbers divides exactly by 3? (a) 1124 (b) 7490 (c) 2572 (d) 6450
38. 38.How many factors does 27 have?
39. 39.What is the smallest number you must take away from 703 so that it divides exactly by 12?
40. 40.What is the smallest number you must add to 653 so that it divides exactly by 12?

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