Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 176 · 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 536 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 111 so that it divides exactly by 13?
3. 3.How many factors does 33 have?
4. 4.Which of these numbers divides exactly by 11? (a) 6284 (b) 2187 (c) 9500 (d) 4840
5. 5.Which of these numbers divides exactly by 9? (a) 2233 (b) 4212 (c) 1464 (d) 7310
6. 6.What is the smallest number you must take away from 440 so that it divides exactly by 3?
7. 7.What is the smallest number you must add to 737 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 374 so that it divides exactly by 8?
9. 9.Which of these numbers divides exactly by 6? (a) 4185 (b) 1837 (c) 5148 (d) 6513
10. 10.What is the smallest number you must take away from 683 so that it divides exactly by 6?
11. 11.What is the smallest number you must add to 106 so that it divides exactly by 13?
12. 12.What is the smallest number you must take away from 795 so that it divides exactly by 6?
13. 13.What is the smallest number you must take away from 340 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 533 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 247 so that it divides exactly by 11?
16. 16.How many factors does 27 have?
17. 17.Which of these numbers divides exactly by 8? (a) 3439 (b) 1593 (c) 5019 (d) 4616
18. 18.How many factors does 92 have?
19. 19.How many factors does 72 have?
20. 20.What is the smallest number you must add to 230 so that it divides exactly by 9?
21. 21.How many factors does 63 have?
22. 22.What is the smallest number you must add to 599 so that it divides exactly by 3?
23. 23.How many factors does 100 have?
24. 24.What is the smallest number you must add to 235 so that it divides exactly by 13?
25. 25.What is the smallest number you must add to 756 so that it divides exactly by 13?
26. 26.Which of these numbers divides exactly by 4? (a) 2306 (b) 9484 (c) 1382 (d) 4855
27. 27.How many factors does 47 have?
28. 28.What is the smallest number you must take away from 266 so that it divides exactly by 3?
29. 29.What is the smallest number you must add to 133 so that it divides exactly by 12?
30. 30.What is the smallest number you must add to 755 so that it divides exactly by 7?
31. 31.How many factors does 23 have?
32. 32.Which of these numbers divides exactly by 11? (a) 2805 (b) 5174 (c) 5903 (d) 4971
33. 33.Which of these numbers divides exactly by 11? (a) 1444 (b) 8006 (c) 9174 (d) 4013
34. 34.How many factors does 45 have?
35. 35.What is the smallest number you must take away from 374 so that it divides exactly by 4?
36. 36.Which of these numbers divides exactly by 3? (a) 1263 (b) 7733 (c) 3080 (d) 7502
37. 37.What is the smallest number you must add to 458 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 8? (a) 4069 (b) 4410 (c) 2164 (d) 6472
39. 39.What is the smallest number you must add to 890 so that it divides exactly by 6?
40. 40.Which of these numbers divides exactly by 4? (a) 8491 (b) 4921 (c) 6646 (d) 9884

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