Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 35 · 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 219 so that it divides exactly by 11?
2. 2.How many factors does 55 have?
3. 3.How many factors does 88 have?
4. 4.How many factors does 61 have?
5. 5.What is the smallest number you must add to 137 so that it divides exactly by 8?
6. 6.What is the smallest number you must add to 206 so that it divides exactly by 4?
7. 7.What is the smallest number you must take away from 306 so that it divides exactly by 4?
8. 8.What is the smallest number you must add to 643 so that it divides exactly by 4?
9. 9.What is the smallest number you must take away from 734 so that it divides exactly by 8?
10. 10.Which of these numbers divides exactly by 4? (a) 8634 (b) 6584 (c) 9035 (d) 3638
11. 11.Which of these numbers divides exactly by 3? (a) 8323 (b) 1374 (c) 8879 (d) 7489
12. 12.How many factors does 13 have?
13. 13.Which of these numbers divides exactly by 4? (a) 9571 (b) 1196 (c) 4217 (d) 6031
14. 14.Which of these numbers divides exactly by 4? (a) 5089 (b) 2750 (c) 8370 (d) 7860
15. 15.What is the smallest number you must add to 838 so that it divides exactly by 6?
16. 16.What is the smallest number you must take away from 402 so that it divides exactly by 7?
17. 17.What is the smallest number you must take away from 475 so that it divides exactly by 6?
18. 18.Which of these numbers divides exactly by 4? (a) 1755 (b) 3735 (c) 8344 (d) 1510
19. 19.Which of these numbers divides exactly by 9? (a) 8157 (b) 7791 (c) 2916 (d) 3272
20. 20.Which of these numbers divides exactly by 8? (a) 7239 (b) 7176 (c) 9021 (d) 1253
21. 21.How many factors does 49 have?
22. 22.How many factors does 100 have?
23. 23.Which of these numbers divides exactly by 8? (a) 8512 (b) 2442 (c) 3961 (d) 3703
24. 24.What is the smallest number you must take away from 215 so that it divides exactly by 13?
25. 25.Which of these numbers divides exactly by 11? (a) 5595 (b) 8252 (c) 8228 (d) 7069
26. 26.What is the smallest number you must add to 329 so that it divides exactly by 13?
27. 27.What is the smallest number you must take away from 570 so that it divides exactly by 8?
28. 28.Which of these numbers divides exactly by 9? (a) 7842 (b) 7315 (c) 7925 (d) 9135
29. 29.What is the smallest number you must add to 712 so that it divides exactly by 9?
30. 30.What is the smallest number you must take away from 137 so that it divides exactly by 12?
31. 31.What is the smallest number you must take away from 326 so that it divides exactly by 4?
32. 32.How many factors does 66 have?
33. 33.Which of these numbers divides exactly by 8? (a) 5225 (b) 5952 (c) 7179 (d) 1501
34. 34.Which of these numbers divides exactly by 6? (a) 4377 (b) 1620 (c) 1581 (d) 1970
35. 35.What is the smallest number you must take away from 101 so that it divides exactly by 9?
36. 36.What is the smallest number you must take away from 643 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 613 so that it divides exactly by 4?
38. 38.What is the smallest number you must take away from 256 so that it divides exactly by 6?
39. 39.What is the smallest number you must take away from 419 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 482 so that it divides exactly by 7?

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