Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 210 · 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 53 have?
2. 2.Which of these numbers divides exactly by 9? (a) 7550 (b) 9310 (c) 5877 (d) 4444
3. 3.Which of these numbers divides exactly by 11? (a) 6630 (b) 2836 (c) 5646 (d) 8932
4. 4.Which of these numbers divides exactly by 4? (a) 6975 (b) 7408 (c) 9574 (d) 8647
5. 5.What is the smallest number you must add to 838 so that it divides exactly by 3?
6. 6.Which of these numbers divides exactly by 9? (a) 4718 (b) 1791 (c) 4951 (d) 5093
7. 7.Which of these numbers divides exactly by 11? (a) 4947 (b) 3454 (c) 1063 (d) 1846
8. 8.What is the smallest number you must add to 130 so that it divides exactly by 6?
9. 9.How many factors does 66 have?
10. 10.What is the smallest number you must add to 374 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 172 so that it divides exactly by 7?
12. 12.Which of these numbers divides exactly by 3? (a) 4600 (b) 6507 (c) 7517 (d) 3179
13. 13.What is the smallest number you must take away from 733 so that it divides exactly by 8?
14. 14.What is the smallest number you must take away from 694 so that it divides exactly by 7?
15. 15.What is the smallest number you must add to 973 so that it divides exactly by 4?
16. 16.What is the smallest number you must add to 465 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 537 so that it divides exactly by 11?
18. 18.How many factors does 95 have?
19. 19.How many factors does 52 have?
20. 20.Which of these numbers divides exactly by 6? (a) 7076 (b) 7661 (c) 3086 (d) 3480
21. 21.Which of these numbers divides exactly by 4? (a) 5045 (b) 5610 (c) 3012 (d) 1510
22. 22.What is the smallest number you must add to 910 so that it divides exactly by 12?
23. 23.What is the smallest number you must take away from 610 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 218 so that it divides exactly by 9?
25. 25.What is the smallest number you must add to 538 so that it divides exactly by 13?
26. 26.How many factors does 68 have?
27. 27.What is the smallest number you must take away from 609 so that it divides exactly by 11?
28. 28.What is the smallest number you must add to 541 so that it divides exactly by 12?
29. 29.What is the smallest number you must add to 633 so that it divides exactly by 7?
30. 30.What is the smallest number you must take away from 243 so that it divides exactly by 12?
31. 31.How many factors does 48 have?
32. 32.What is the smallest number you must add to 262 so that it divides exactly by 7?
33. 33.What is the smallest number you must take away from 641 so that it divides exactly by 3?
34. 34.Which of these numbers divides exactly by 6? (a) 7432 (b) 1419 (c) 9090 (d) 2206
35. 35.How many factors does 85 have?
36. 36.What is the smallest number you must take away from 935 so that it divides exactly by 6?
37. 37.What is the smallest number you must add to 533 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 559 so that it divides exactly by 7?
39. 39.Which of these numbers divides exactly by 3? (a) 2575 (b) 4427 (c) 4511 (d) 9759
40. 40.What is the smallest number you must add to 307 so that it divides exactly by 6?

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