Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 311 · 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 38 have?
2. 2.Which of these numbers divides exactly by 4? (a) 2375 (b) 4515 (c) 7312 (d) 1991
3. 3.How many factors does 27 have?
4. 4.How many factors does 13 have?
5. 5.What is the smallest number you must take away from 358 so that it divides exactly by 7?
6. 6.What is the smallest number you must add to 807 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 8? (a) 2144 (b) 4642 (c) 8291 (d) 1089
8. 8.Which of these numbers divides exactly by 6? (a) 2022 (b) 5139 (c) 2181 (d) 7418
9. 9.How many factors does 47 have?
10. 10.Which of these numbers divides exactly by 6? (a) 2342 (b) 9177 (c) 3715 (d) 4518
11. 11.What is the smallest number you must take away from 956 so that it divides exactly by 7?
12. 12.What is the smallest number you must take away from 218 so that it divides exactly by 7?
13. 13.What is the smallest number you must take away from 685 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 433 so that it divides exactly by 11?
15. 15.How many factors does 74 have?
16. 16.What is the smallest number you must take away from 643 so that it divides exactly by 9?
17. 17.What is the smallest number you must add to 137 so that it divides exactly by 13?
18. 18.How many factors does 20 have?
19. 19.What is the smallest number you must add to 663 so that it divides exactly by 8?
20. 20.What is the smallest number you must add to 371 so that it divides exactly by 4?
21. 21.What is the smallest number you must add to 807 so that it divides exactly by 4?
22. 22.How many factors does 31 have?
23. 23.What is the smallest number you must add to 203 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 353 so that it divides exactly by 9?
25. 25.What is the smallest number you must take away from 211 so that it divides exactly by 13?
26. 26.What is the smallest number you must add to 304 so that it divides exactly by 12?
27. 27.What is the smallest number you must add to 982 so that it divides exactly by 11?
28. 28.What is the smallest number you must add to 187 so that it divides exactly by 6?
29. 29.How many factors does 25 have?
30. 30.How many factors does 71 have?
31. 31.Which of these numbers divides exactly by 9? (a) 8780 (b) 7112 (c) 1588 (d) 4392
32. 32.What is the smallest number you must add to 626 so that it divides exactly by 11?
33. 33.What is the smallest number you must add to 794 so that it divides exactly by 8?
34. 34.What is the smallest number you must take away from 751 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 9? (a) 7588 (b) 5489 (c) 1537 (d) 3942
36. 36.Which of these numbers divides exactly by 6? (a) 4150 (b) 1224 (c) 6544 (d) 8660
37. 37.What is the smallest number you must add to 832 so that it divides exactly by 9?
38. 38.What is the smallest number you must take away from 752 so that it divides exactly by 9?
39. 39.What is the smallest number you must add to 904 so that it divides exactly by 7?
40. 40.What is the smallest number you must add to 805 so that it divides exactly by 4?

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