Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 279 · 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.Which of these numbers divides exactly by 8? (a) 3347 (b) 1780 (c) 4433 (d) 5472
2. 2.What is the smallest number you must add to 745 so that it divides exactly by 7?
3. 3.Which of these numbers divides exactly by 6? (a) 1814 (b) 8664 (c) 1042 (d) 1309
4. 4.What is the smallest number you must add to 407 so that it divides exactly by 8?
5. 5.What is the smallest number you must take away from 517 so that it divides exactly by 6?
6. 6.How many factors does 18 have?
7. 7.How many factors does 85 have?
8. 8.What is the smallest number you must add to 529 so that it divides exactly by 7?
9. 9.What is the smallest number you must add to 531 so that it divides exactly by 7?
10. 10.How many factors does 32 have?
11. 11.What is the smallest number you must take away from 272 so that it divides exactly by 3?
12. 12.Which of these numbers divides exactly by 4? (a) 1536 (b) 9661 (c) 7725 (d) 2907
13. 13.Which of these numbers divides exactly by 8? (a) 1064 (b) 4962 (c) 9169 (d) 6731
14. 14.What is the smallest number you must add to 560 so that it divides exactly by 9?
15. 15.Which of these numbers divides exactly by 3? (a) 4735 (b) 5319 (c) 9284 (d) 6670
16. 16.What is the smallest number you must take away from 460 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 4? (a) 7826 (b) 1351 (c) 9241 (d) 2656
18. 18.What is the smallest number you must add to 125 so that it divides exactly by 11?
19. 19.What is the smallest number you must add to 781 so that it divides exactly by 13?
20. 20.What is the smallest number you must add to 117 so that it divides exactly by 6?
21. 21.What is the smallest number you must take away from 345 so that it divides exactly by 8?
22. 22.Which of these numbers divides exactly by 6? (a) 2849 (b) 7619 (c) 5661 (d) 4758
23. 23.What is the smallest number you must add to 999 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 6? (a) 2285 (b) 7483 (c) 3522 (d) 4665
25. 25.How many factors does 34 have?
26. 26.How many factors does 13 have?
27. 27.What is the smallest number you must add to 107 so that it divides exactly by 13?
28. 28.What is the smallest number you must add to 117 so that it divides exactly by 4?
29. 29.What is the smallest number you must add to 233 so that it divides exactly by 4?
30. 30.What is the smallest number you must take away from 304 so that it divides exactly by 6?
31. 31.How many factors does 28 have?
32. 32.Which of these numbers divides exactly by 4? (a) 5934 (b) 2634 (c) 4586 (d) 6816
33. 33.Which of these numbers divides exactly by 3? (a) 7588 (b) 7596 (c) 9092 (d) 4567
34. 34.What is the smallest number you must add to 515 so that it divides exactly by 13?
35. 35.What is the smallest number you must take away from 987 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 9? (a) 3510 (b) 5591 (c) 9028 (d) 2840
37. 37.How many factors does 75 have?
38. 38.What is the smallest number you must add to 297 so that it divides exactly by 4?
39. 39.Which of these numbers divides exactly by 8? (a) 1324 (b) 4904 (c) 7141 (d) 4303
40. 40.Which of these numbers divides exactly by 6? (a) 7534 (b) 9916 (c) 5235 (d) 4356

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