Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 315 · 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 56 have?
2. 2.What is the smallest number you must take away from 493 so that it divides exactly by 6?
3. 3.How many factors does 29 have?
4. 4.What is the smallest number you must add to 150 so that it divides exactly by 11?
5. 5.How many factors does 21 have?
6. 6.What is the smallest number you must add to 569 so that it divides exactly by 12?
7. 7.How many factors does 55 have?
8. 8.What is the smallest number you must add to 443 so that it divides exactly by 9?
9. 9.What is the smallest number you must take away from 761 so that it divides exactly by 9?
10. 10.How many factors does 73 have?
11. 11.What is the smallest number you must add to 227 so that it divides exactly by 6?
12. 12.What is the smallest number you must add to 155 so that it divides exactly by 6?
13. 13.How many factors does 72 have?
14. 14.Which of these numbers divides exactly by 3? (a) 2482 (b) 7010 (c) 3221 (d) 5871
15. 15.What is the smallest number you must add to 340 so that it divides exactly by 8?
16. 16.What is the smallest number you must add to 314 so that it divides exactly by 12?
17. 17.What is the smallest number you must add to 117 so that it divides exactly by 8?
18. 18.What is the smallest number you must add to 460 so that it divides exactly by 9?
19. 19.Which of these numbers divides exactly by 8? (a) 8063 (b) 4761 (c) 6412 (d) 9744
20. 20.Which of these numbers divides exactly by 4? (a) 8455 (b) 3683 (c) 4367 (d) 3228
21. 21.What is the smallest number you must take away from 555 so that it divides exactly by 8?
22. 22.Which of these numbers divides exactly by 9? (a) 8556 (b) 9890 (c) 1512 (d) 3471
23. 23.How many factors does 97 have?
24. 24.What is the smallest number you must take away from 289 so that it divides exactly by 11?
25. 25.Which of these numbers divides exactly by 11? (a) 6894 (b) 9020 (c) 5415 (d) 3357
26. 26.What is the smallest number you must take away from 118 so that it divides exactly by 12?
27. 27.What is the smallest number you must take away from 181 so that it divides exactly by 12?
28. 28.Which of these numbers divides exactly by 3? (a) 8528 (b) 2449 (c) 7928 (d) 8949
29. 29.What is the smallest number you must add to 907 so that it divides exactly by 6?
30. 30.What is the smallest number you must take away from 787 so that it divides exactly by 12?
31. 31.What is the smallest number you must take away from 526 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 4? (a) 5751 (b) 5809 (c) 7826 (d) 2244
33. 33.How many factors does 96 have?
34. 34.What is the smallest number you must add to 103 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 3? (a) 1024 (b) 9165 (c) 3529 (d) 4046
36. 36.Which of these numbers divides exactly by 11? (a) 9028 (b) 8104 (c) 3399 (d) 8119
37. 37.How many factors does 82 have?
38. 38.Which of these numbers divides exactly by 6? (a) 2093 (b) 2223 (c) 3078 (d) 7318
39. 39.What is the smallest number you must add to 560 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 356 so that it divides exactly by 6?

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