Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 215 · 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.Which of these numbers divides exactly by 9? (a) 2225 (b) 5415 (c) 7952 (d) 6759
2. 2.What is the smallest number you must add to 430 so that it divides exactly by 9?
3. 3.What is the smallest number you must take away from 772 so that it divides exactly by 9?
4. 4.How many factors does 21 have?
5. 5.What is the smallest number you must take away from 668 so that it divides exactly by 9?
6. 6.What is the smallest number you must add to 843 so that it divides exactly by 6?
7. 7.How many factors does 98 have?
8. 8.Which of these numbers divides exactly by 6? (a) 7701 (b) 1296 (c) 9740 (d) 3253
9. 9.How many factors does 16 have?
10. 10.How many factors does 19 have?
11. 11.What is the smallest number you must take away from 694 so that it divides exactly by 9?
12. 12.How many factors does 47 have?
13. 13.What is the smallest number you must take away from 434 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 441 so that it divides exactly by 13?
15. 15.What is the smallest number you must take away from 677 so that it divides exactly by 4?
16. 16.How many factors does 40 have?
17. 17.What is the smallest number you must add to 221 so that it divides exactly by 6?
18. 18.Which of these numbers divides exactly by 3? (a) 7703 (b) 4295 (c) 3353 (d) 4719
19. 19.What is the smallest number you must take away from 227 so that it divides exactly by 4?
20. 20.Which of these numbers divides exactly by 9? (a) 4896 (b) 1131 (c) 1536 (d) 4310
21. 21.How many factors does 87 have?
22. 22.How many factors does 99 have?
23. 23.What is the smallest number you must add to 458 so that it divides exactly by 13?
24. 24.What is the smallest number you must add to 929 so that it divides exactly by 11?
25. 25.What is the smallest number you must add to 555 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 9? (a) 2332 (b) 2975 (c) 2610 (d) 3594
27. 27.How many factors does 82 have?
28. 28.What is the smallest number you must add to 341 so that it divides exactly by 13?
29. 29.Which of these numbers divides exactly by 3? (a) 9635 (b) 2383 (c) 6621 (d) 9242
30. 30.What is the smallest number you must take away from 417 so that it divides exactly by 9?
31. 31.What is the smallest number you must take away from 831 so that it divides exactly by 6?
32. 32.What is the smallest number you must take away from 614 so that it divides exactly by 12?
33. 33.What is the smallest number you must add to 958 so that it divides exactly by 9?
34. 34.What is the smallest number you must take away from 321 so that it divides exactly by 12?
35. 35.What is the smallest number you must take away from 593 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 919 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 529 so that it divides exactly by 8?
38. 38.Which of these numbers divides exactly by 3? (a) 8415 (b) 8986 (c) 7670 (d) 5017
39. 39.What is the smallest number you must add to 166 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 107 so that it divides exactly by 3?

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