Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 56 · 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 841 so that it divides exactly by 7?
2. 2.What is the smallest number you must add to 738 so that it divides exactly by 4?
3. 3.Which of these numbers divides exactly by 8? (a) 8168 (b) 6620 (c) 8521 (d) 8014
4. 4.What is the smallest number you must add to 927 so that it divides exactly by 8?
5. 5.Which of these numbers divides exactly by 4? (a) 6607 (b) 4502 (c) 6082 (d) 6884
6. 6.What is the smallest number you must take away from 806 so that it divides exactly by 12?
7. 7.What is the smallest number you must add to 301 so that it divides exactly by 6?
8. 8.How many factors does 14 have?
9. 9.What is the smallest number you must add to 173 so that it divides exactly by 6?
10. 10.Which of these numbers divides exactly by 9? (a) 3836 (b) 6684 (c) 4782 (d) 9522
11. 11.How many factors does 49 have?
12. 12.What is the smallest number you must add to 125 so that it divides exactly by 13?
13. 13.What is the smallest number you must add to 387 so that it divides exactly by 6?
14. 14.What is the smallest number you must add to 230 so that it divides exactly by 12?
15. 15.Which of these numbers divides exactly by 9? (a) 3178 (b) 3618 (c) 3013 (d) 2947
16. 16.What is the smallest number you must add to 406 so that it divides exactly by 3?
17. 17.What is the smallest number you must take away from 778 so that it divides exactly by 3?
18. 18.What is the smallest number you must take away from 843 so that it divides exactly by 6?
19. 19.How many factors does 82 have?
20. 20.What is the smallest number you must take away from 861 so that it divides exactly by 11?
21. 21.Which of these numbers divides exactly by 9? (a) 2840 (b) 8649 (c) 6837 (d) 8236
22. 22.What is the smallest number you must add to 397 so that it divides exactly by 7?
23. 23.What is the smallest number you must take away from 967 so that it divides exactly by 4?
24. 24.How many factors does 91 have?
25. 25.What is the smallest number you must take away from 809 so that it divides exactly by 11?
26. 26.How many factors does 90 have?
27. 27.How many factors does 43 have?
28. 28.Which of these numbers divides exactly by 3? (a) 9493 (b) 7774 (c) 7260 (d) 9559
29. 29.Which of these numbers divides exactly by 4? (a) 7888 (b) 9322 (c) 5123 (d) 9613
30. 30.What is the smallest number you must take away from 440 so that it divides exactly by 7?
31. 31.What is the smallest number you must add to 513 so that it divides exactly by 12?
32. 32.Which of these numbers divides exactly by 4? (a) 6690 (b) 1528 (c) 2369 (d) 8114
33. 33.How many factors does 18 have?
34. 34.How many factors does 15 have?
35. 35.How many factors does 57 have?
36. 36.What is the smallest number you must add to 471 so that it divides exactly by 11?
37. 37.What is the smallest number you must take away from 308 so that it divides exactly by 12?
38. 38.What is the smallest number you must add to 761 so that it divides exactly by 3?
39. 39.Which of these numbers divides exactly by 4? (a) 4381 (b) 4927 (c) 9924 (d) 2605
40. 40.What is the smallest number you must take away from 713 so that it divides exactly by 12?

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