Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 99 · 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 262 so that it divides exactly by 8?
2. 2.Which of these numbers divides exactly by 8? (a) 1188 (b) 9212 (c) 3374 (d) 8024
3. 3.How many factors does 59 have?
4. 4.How many factors does 39 have?
5. 5.How many factors does 47 have?
6. 6.What is the smallest number you must take away from 650 so that it divides exactly by 11?
7. 7.Which of these numbers divides exactly by 8? (a) 1101 (b) 6472 (c) 3276 (d) 6154
8. 8.What is the smallest number you must add to 992 so that it divides exactly by 7?
9. 9.Which of these numbers divides exactly by 8? (a) 2216 (b) 8069 (c) 7215 (d) 1281
10. 10.What is the smallest number you must add to 741 so that it divides exactly by 11?
11. 11.Which of these numbers divides exactly by 4? (a) 7634 (b) 3104 (c) 8638 (d) 1965
12. 12.How many factors does 89 have?
13. 13.What is the smallest number you must add to 167 so that it divides exactly by 13?
14. 14.How many factors does 21 have?
15. 15.What is the smallest number you must take away from 168 so that it divides exactly by 11?
16. 16.What is the smallest number you must take away from 204 so that it divides exactly by 11?
17. 17.How many factors does 95 have?
18. 18.Which of these numbers divides exactly by 8? (a) 3243 (b) 5360 (c) 3087 (d) 4229
19. 19.Which of these numbers divides exactly by 8? (a) 9018 (b) 3678 (c) 8976 (d) 4821
20. 20.How many factors does 48 have?
21. 21.What is the smallest number you must take away from 578 so that it divides exactly by 8?
22. 22.Which of these numbers divides exactly by 8? (a) 1840 (b) 9621 (c) 7548 (d) 8017
23. 23.Which of these numbers divides exactly by 6? (a) 6857 (b) 7993 (c) 7572 (d) 9430
24. 24.What is the smallest number you must take away from 406 so that it divides exactly by 8?
25. 25.Which of these numbers divides exactly by 3? (a) 8471 (b) 8698 (c) 7008 (d) 9937
26. 26.What is the smallest number you must add to 393 so that it divides exactly by 13?
27. 27.How many factors does 16 have?
28. 28.What is the smallest number you must add to 686 so that it divides exactly by 6?
29. 29.What is the smallest number you must take away from 122 so that it divides exactly by 7?
30. 30.How many factors does 42 have?
31. 31.What is the smallest number you must add to 682 so that it divides exactly by 4?
32. 32.How many factors does 61 have?
33. 33.Which of these numbers divides exactly by 8? (a) 1227 (b) 8096 (c) 9497 (d) 9580
34. 34.What is the smallest number you must add to 724 so that it divides exactly by 7?
35. 35.What is the smallest number you must take away from 650 so that it divides exactly by 12?
36. 36.What is the smallest number you must take away from 102 so that it divides exactly by 8?
37. 37.What is the smallest number you must take away from 761 so that it divides exactly by 4?
38. 38.What is the smallest number you must take away from 838 so that it divides exactly by 13?
39. 39.Which of these numbers divides exactly by 9? (a) 2846 (b) 9604 (c) 4162 (d) 4716
40. 40.How many factors does 93 have?

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