Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 245 · 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 266 so that it divides exactly by 12?
2. 2.Which of these numbers divides exactly by 3? (a) 7792 (b) 1827 (c) 2159 (d) 9680
3. 3.How many factors does 100 have?
4. 4.How many factors does 64 have?
5. 5.Which of these numbers divides exactly by 6? (a) 7940 (b) 4276 (c) 7443 (d) 5298
6. 6.What is the smallest number you must take away from 273 so that it divides exactly by 4?
7. 7.What is the smallest number you must take away from 342 so that it divides exactly by 4?
8. 8.What is the smallest number you must take away from 286 so that it divides exactly by 6?
9. 9.How many factors does 73 have?
10. 10.What is the smallest number you must take away from 117 so that it divides exactly by 4?
11. 11.What is the smallest number you must add to 607 so that it divides exactly by 6?
12. 12.What is the smallest number you must take away from 870 so that it divides exactly by 9?
13. 13.What is the smallest number you must add to 606 so that it divides exactly by 12?
14. 14.Which of these numbers divides exactly by 11? (a) 3476 (b) 2540 (c) 1976 (d) 2686
15. 15.Which of these numbers divides exactly by 3? (a) 1657 (b) 1107 (c) 1871 (d) 8641
16. 16.Which of these numbers divides exactly by 6? (a) 2939 (b) 4837 (c) 8172 (d) 2455
17. 17.Which of these numbers divides exactly by 9? (a) 4043 (b) 7308 (c) 5387 (d) 5488
18. 18.How many factors does 71 have?
19. 19.What is the smallest number you must take away from 302 so that it divides exactly by 7?
20. 20.Which of these numbers divides exactly by 4? (a) 6305 (b) 8923 (c) 2352 (d) 4038
21. 21.Which of these numbers divides exactly by 11? (a) 1245 (b) 7300 (c) 2673 (d) 6832
22. 22.How many factors does 40 have?
23. 23.Which of these numbers divides exactly by 8? (a) 3229 (b) 8016 (c) 1106 (d) 1412
24. 24.How many factors does 68 have?
25. 25.Which of these numbers divides exactly by 3? (a) 3509 (b) 9688 (c) 9455 (d) 3069
26. 26.What is the smallest number you must add to 894 so that it divides exactly by 12?
27. 27.Which of these numbers divides exactly by 3? (a) 9460 (b) 1276 (c) 7856 (d) 3033
28. 28.What is the smallest number you must take away from 899 so that it divides exactly by 12?
29. 29.What is the smallest number you must take away from 406 so that it divides exactly by 11?
30. 30.What is the smallest number you must take away from 979 so that it divides exactly by 6?
31. 31.What is the smallest number you must add to 478 so that it divides exactly by 3?
32. 32.What is the smallest number you must add to 428 so that it divides exactly by 13?
33. 33.What is the smallest number you must add to 109 so that it divides exactly by 13?
34. 34.How many factors does 34 have?
35. 35.What is the smallest number you must take away from 850 so that it divides exactly by 11?
36. 36.Which of these numbers divides exactly by 3? (a) 7698 (b) 1090 (c) 1952 (d) 8399
37. 37.What is the smallest number you must take away from 403 so that it divides exactly by 8?
38. 38.What is the smallest number you must add to 515 so that it divides exactly by 11?
39. 39.What is the smallest number you must take away from 503 so that it divides exactly by 4?
40. 40.Which of these numbers divides exactly by 3? (a) 6515 (b) 4129 (c) 1754 (d) 3945

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