Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 87 · 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 883 so that it divides exactly by 11?
2. 2.Which of these numbers divides exactly by 9? (a) 3929 (b) 1111 (c) 4554 (d) 1981
3. 3.How many factors does 97 have?
4. 4.What is the smallest number you must add to 498 so that it divides exactly by 9?
5. 5.What is the smallest number you must add to 821 so that it divides exactly by 12?
6. 6.What is the smallest number you must add to 832 so that it divides exactly by 9?
7. 7.Which of these numbers divides exactly by 4? (a) 3373 (b) 8756 (c) 5654 (d) 9109
8. 8.How many factors does 30 have?
9. 9.What is the smallest number you must take away from 254 so that it divides exactly by 8?
10. 10.What is the smallest number you must take away from 853 so that it divides exactly by 9?
11. 11.How many factors does 31 have?
12. 12.How many factors does 84 have?
13. 13.Which of these numbers divides exactly by 6? (a) 3038 (b) 3620 (c) 6180 (d) 7694
14. 14.Which of these numbers divides exactly by 3? (a) 3763 (b) 7633 (c) 6837 (d) 1123
15. 15.Which of these numbers divides exactly by 3? (a) 6617 (b) 1237 (c) 1316 (d) 1629
16. 16.How many factors does 44 have?
17. 17.What is the smallest number you must add to 742 so that it divides exactly by 11?
18. 18.What is the smallest number you must take away from 411 so that it divides exactly by 6?
19. 19.How many factors does 40 have?
20. 20.How many factors does 15 have?
21. 21.What is the smallest number you must take away from 923 so that it divides exactly by 3?
22. 22.Which of these numbers divides exactly by 8? (a) 6228 (b) 3118 (c) 3016 (d) 1549
23. 23.What is the smallest number you must take away from 878 so that it divides exactly by 3?
24. 24.How many factors does 24 have?
25. 25.What is the smallest number you must take away from 275 so that it divides exactly by 8?
26. 26.Which of these numbers divides exactly by 6? (a) 3514 (b) 2067 (c) 8728 (d) 7842
27. 27.How many factors does 58 have?
28. 28.How many factors does 13 have?
29. 29.What is the smallest number you must take away from 892 so that it divides exactly by 13?
30. 30.What is the smallest number you must take away from 630 so that it divides exactly by 11?
31. 31.What is the smallest number you must take away from 211 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 463 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 6? (a) 7563 (b) 6151 (c) 3522 (d) 5590
34. 34.What is the smallest number you must take away from 251 so that it divides exactly by 11?
35. 35.What is the smallest number you must take away from 174 so that it divides exactly by 9?
36. 36.What is the smallest number you must take away from 230 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 433 so that it divides exactly by 9?
38. 38.What is the smallest number you must add to 984 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 754 so that it divides exactly by 6?
40. 40.What is the smallest number you must add to 212 so that it divides exactly by 13?

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