Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 281 · 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 761 so that it divides exactly by 7?
2. 2.What is the smallest number you must take away from 822 so that it divides exactly by 8?
3. 3.What is the smallest number you must add to 244 so that it divides exactly by 12?
4. 4.How many factors does 38 have?
5. 5.What is the smallest number you must take away from 614 so that it divides exactly by 9?
6. 6.What is the smallest number you must add to 415 so that it divides exactly by 7?
7. 7.What is the smallest number you must add to 599 so that it divides exactly by 12?
8. 8.Which of these numbers divides exactly by 6? (a) 4219 (b) 1758 (c) 1640 (d) 7065
9. 9.What is the smallest number you must take away from 410 so that it divides exactly by 11?
10. 10.Which of these numbers divides exactly by 3? (a) 7461 (b) 8641 (c) 3953 (d) 5648
11. 11.How many factors does 48 have?
12. 12.What is the smallest number you must take away from 303 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 181 so that it divides exactly by 6?
14. 14.How many factors does 95 have?
15. 15.Which of these numbers divides exactly by 11? (a) 7576 (b) 7468 (c) 4038 (d) 2563
16. 16.How many factors does 19 have?
17. 17.Which of these numbers divides exactly by 9? (a) 8220 (b) 2973 (c) 8521 (d) 8442
18. 18.What is the smallest number you must add to 205 so that it divides exactly by 12?
19. 19.Which of these numbers divides exactly by 3? (a) 4208 (b) 1095 (c) 4885 (d) 1333
20. 20.What is the smallest number you must add to 568 so that it divides exactly by 11?
21. 21.Which of these numbers divides exactly by 4? (a) 9916 (b) 1183 (c) 2461 (d) 5269
22. 22.What is the smallest number you must take away from 346 so that it divides exactly by 9?
23. 23.Which of these numbers divides exactly by 4? (a) 4215 (b) 1410 (c) 1756 (d) 1773
24. 24.How many factors does 75 have?
25. 25.How many factors does 93 have?
26. 26.Which of these numbers divides exactly by 9? (a) 5092 (b) 6156 (c) 5785 (d) 6954
27. 27.What is the smallest number you must add to 284 so that it divides exactly by 13?
28. 28.How many factors does 64 have?
29. 29.What is the smallest number you must take away from 354 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 8? (a) 1052 (b) 6141 (c) 8489 (d) 5144
31. 31.How many factors does 78 have?
32. 32.Which of these numbers divides exactly by 3? (a) 5158 (b) 4831 (c) 3660 (d) 4916
33. 33.How many factors does 14 have?
34. 34.How many factors does 71 have?
35. 35.What is the smallest number you must take away from 319 so that it divides exactly by 9?
36. 36.What is the smallest number you must add to 309 so that it divides exactly by 13?
37. 37.Which of these numbers divides exactly by 8? (a) 2976 (b) 3550 (c) 8092 (d) 8382
38. 38.What is the smallest number you must take away from 223 so that it divides exactly by 3?
39. 39.Which of these numbers divides exactly by 11? (a) 1264 (b) 5643 (c) 5415 (d) 9978
40. 40.How many factors does 17 have?

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