Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 269 · 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 608 so that it divides exactly by 13?
2. 2.What is the smallest number you must add to 423 so that it divides exactly by 4?
3. 3.What is the smallest number you must take away from 289 so that it divides exactly by 3?
4. 4.What is the smallest number you must add to 213 so that it divides exactly by 13?
5. 5.How many factors does 33 have?
6. 6.What is the smallest number you must add to 177 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 394 so that it divides exactly by 7?
8. 8.How many factors does 82 have?
9. 9.How many factors does 81 have?
10. 10.What is the smallest number you must add to 112 so that it divides exactly by 9?
11. 11.How many factors does 55 have?
12. 12.What is the smallest number you must add to 638 so that it divides exactly by 13?
13. 13.What is the smallest number you must add to 416 so that it divides exactly by 9?
14. 14.How many factors does 78 have?
15. 15.Which of these numbers divides exactly by 9? (a) 7774 (b) 4642 (c) 6115 (d) 6453
16. 16.What is the smallest number you must add to 197 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 477 so that it divides exactly by 4?
18. 18.Which of these numbers divides exactly by 9? (a) 9269 (b) 6318 (c) 7241 (d) 2852
19. 19.What is the smallest number you must add to 338 so that it divides exactly by 7?
20. 20.Which of these numbers divides exactly by 8? (a) 1988 (b) 2406 (c) 6688 (d) 7163
21. 21.How many factors does 35 have?
22. 22.Which of these numbers divides exactly by 6? (a) 8898 (b) 3531 (c) 9799 (d) 1853
23. 23.What is the smallest number you must take away from 603 so that it divides exactly by 8?
24. 24.How many factors does 12 have?
25. 25.How many factors does 64 have?
26. 26.Which of these numbers divides exactly by 11? (a) 1821 (b) 3733 (c) 8866 (d) 8713
27. 27.What is the smallest number you must add to 301 so that it divides exactly by 13?
28. 28.How many factors does 72 have?
29. 29.What is the smallest number you must add to 996 so that it divides exactly by 8?
30. 30.How many factors does 49 have?
31. 31.Which of these numbers divides exactly by 8? (a) 5596 (b) 6802 (c) 8582 (d) 7056
32. 32.What is the smallest number you must add to 119 so that it divides exactly by 9?
33. 33.How many factors does 58 have?
34. 34.What is the smallest number you must add to 571 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 981 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 471 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 437 so that it divides exactly by 7?
38. 38.How many factors does 71 have?
39. 39.What is the smallest number you must take away from 331 so that it divides exactly by 7?
40. 40.What is the smallest number you must take away from 347 so that it divides exactly by 8?

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