Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 132 · 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 719 so that it divides exactly by 8?
2. 2.What is the smallest number you must add to 174 so that it divides exactly by 13?
3. 3.What is the smallest number you must take away from 820 so that it divides exactly by 13?
4. 4.What is the smallest number you must add to 976 so that it divides exactly by 6?
5. 5.What is the smallest number you must add to 631 so that it divides exactly by 6?
6. 6.What is the smallest number you must add to 547 so that it divides exactly by 8?
7. 7.What is the smallest number you must take away from 725 so that it divides exactly by 6?
8. 8.Which of these numbers divides exactly by 11? (a) 3652 (b) 6196 (c) 1315 (d) 5329
9. 9.What is the smallest number you must take away from 339 so that it divides exactly by 7?
10. 10.What is the smallest number you must add to 483 so that it divides exactly by 9?
11. 11.What is the smallest number you must take away from 229 so that it divides exactly by 6?
12. 12.What is the smallest number you must add to 863 so that it divides exactly by 11?
13. 13.Which of these numbers divides exactly by 4? (a) 2249 (b) 9093 (c) 2093 (d) 9808
14. 14.Which of these numbers divides exactly by 9? (a) 5365 (b) 2692 (c) 5112 (d) 8147
15. 15.What is the smallest number you must add to 474 so that it divides exactly by 11?
16. 16.How many factors does 62 have?
17. 17.How many factors does 63 have?
18. 18.Which of these numbers divides exactly by 3? (a) 8816 (b) 7840 (c) 7965 (d) 5885
19. 19.Which of these numbers divides exactly by 6? (a) 6676 (b) 3297 (c) 3237 (d) 4470
20. 20.How many factors does 90 have?
21. 21.What is the smallest number you must add to 740 so that it divides exactly by 7?
22. 22.Which of these numbers divides exactly by 11? (a) 1486 (b) 6518 (c) 1118 (d) 4301
23. 23.How many factors does 41 have?
24. 24.How many factors does 17 have?
25. 25.What is the smallest number you must take away from 222 so that it divides exactly by 4?
26. 26.What is the smallest number you must add to 998 so that it divides exactly by 4?
27. 27.What is the smallest number you must add to 226 so that it divides exactly by 13?
28. 28.How many factors does 22 have?
29. 29.What is the smallest number you must add to 691 so that it divides exactly by 7?
30. 30.What is the smallest number you must add to 546 so that it divides exactly by 4?
31. 31.How many factors does 44 have?
32. 32.Which of these numbers divides exactly by 9? (a) 3700 (b) 7042 (c) 2032 (d) 5175
33. 33.What is the smallest number you must add to 675 so that it divides exactly by 7?
34. 34.What is the smallest number you must add to 389 so that it divides exactly by 13?
35. 35.How many factors does 69 have?
36. 36.What is the smallest number you must add to 915 so that it divides exactly by 7?
37. 37.What is the smallest number you must take away from 189 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 983 so that it divides exactly by 9?
39. 39.What is the smallest number you must add to 718 so that it divides exactly by 7?
40. 40.Which of these numbers divides exactly by 9? (a) 3168 (b) 7280 (c) 7797 (d) 7340

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