Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 22 · 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.How many factors does 12 have?
2. 2.What is the smallest number you must take away from 957 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 518 so that it divides exactly by 8?
4. 4.Which of these numbers divides exactly by 4? (a) 4427 (b) 4127 (c) 7604 (d) 3637
5. 5.How many factors does 95 have?
6. 6.What is the smallest number you must take away from 189 so that it divides exactly by 8?
7. 7.How many factors does 35 have?
8. 8.Which of these numbers divides exactly by 6? (a) 2792 (b) 1325 (c) 8748 (d) 3825
9. 9.Which of these numbers divides exactly by 3? (a) 1227 (b) 2291 (c) 5446 (d) 9512
10. 10.What is the smallest number you must add to 145 so that it divides exactly by 4?
11. 11.What is the smallest number you must take away from 533 so that it divides exactly by 12?
12. 12.What is the smallest number you must add to 707 so that it divides exactly by 4?
13. 13.What is the smallest number you must take away from 114 so that it divides exactly by 8?
14. 14.Which of these numbers divides exactly by 8? (a) 8668 (b) 8536 (c) 7604 (d) 1526
15. 15.How many factors does 67 have?
16. 16.What is the smallest number you must take away from 120 so that it divides exactly by 13?
17. 17.What is the smallest number you must take away from 707 so that it divides exactly by 13?
18. 18.How many factors does 83 have?
19. 19.How many factors does 41 have?
20. 20.What is the smallest number you must add to 689 so that it divides exactly by 3?
21. 21.What is the smallest number you must take away from 190 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 510 so that it divides exactly by 11?
23. 23.What is the smallest number you must take away from 109 so that it divides exactly by 12?
24. 24.How many factors does 100 have?
25. 25.Which of these numbers divides exactly by 11? (a) 9167 (b) 9860 (c) 6957 (d) 4983
26. 26.Which of these numbers divides exactly by 9? (a) 1620 (b) 9173 (c) 2035 (d) 4218
27. 27.What is the smallest number you must take away from 915 so that it divides exactly by 9?
28. 28.How many factors does 38 have?
29. 29.What is the smallest number you must take away from 347 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 11? (a) 4376 (b) 5567 (c) 9900 (d) 7501
31. 31.How many factors does 51 have?
32. 32.How many factors does 43 have?
33. 33.What is the smallest number you must take away from 991 so that it divides exactly by 3?
34. 34.Which of these numbers divides exactly by 9? (a) 5736 (b) 4226 (c) 8379 (d) 6972
35. 35.What is the smallest number you must add to 833 so that it divides exactly by 13?
36. 36.What is the smallest number you must add to 829 so that it divides exactly by 9?
37. 37.What is the smallest number you must take away from 678 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 6? (a) 9628 (b) 1476 (c) 6461 (d) 4665
39. 39.Which of these numbers divides exactly by 3? (a) 3557 (b) 1670 (c) 1715 (d) 9033
40. 40.Which of these numbers divides exactly by 11? (a) 6795 (b) 8437 (c) 3940 (d) 5550

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