Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 92 · 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 860 so that it divides exactly by 13?
2. 2.What is the smallest number you must add to 163 so that it divides exactly by 6?
3. 3.How many factors does 47 have?
4. 4.Which of these numbers divides exactly by 3? (a) 9480 (b) 3575 (c) 4744 (d) 7736
5. 5.How many factors does 39 have?
6. 6.How many factors does 30 have?
7. 7.What is the smallest number you must take away from 248 so that it divides exactly by 12?
8. 8.Which of these numbers divides exactly by 11? (a) 2856 (b) 7806 (c) 3124 (d) 3053
9. 9.How many factors does 41 have?
10. 10.How many factors does 79 have?
11. 11.What is the smallest number you must take away from 467 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 6? (a) 4808 (b) 7402 (c) 5688 (d) 3370
13. 13.What is the smallest number you must take away from 401 so that it divides exactly by 8?
14. 14.How many factors does 62 have?
15. 15.What is the smallest number you must take away from 226 so that it divides exactly by 4?
16. 16.What is the smallest number you must take away from 843 so that it divides exactly by 6?
17. 17.What is the smallest number you must take away from 502 so that it divides exactly by 9?
18. 18.How many factors does 31 have?
19. 19.What is the smallest number you must take away from 734 so that it divides exactly by 3?
20. 20.What is the smallest number you must take away from 997 so that it divides exactly by 9?
21. 21.How many factors does 68 have?
22. 22.What is the smallest number you must add to 196 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 262 so that it divides exactly by 8?
24. 24.How many factors does 17 have?
25. 25.What is the smallest number you must add to 432 so that it divides exactly by 11?
26. 26.Which of these numbers divides exactly by 4? (a) 2256 (b) 8794 (c) 2197 (d) 6271
27. 27.What is the smallest number you must add to 370 so that it divides exactly by 7?
28. 28.How many factors does 52 have?
29. 29.How many factors does 82 have?
30. 30.What is the smallest number you must add to 494 so that it divides exactly by 6?
31. 31.What is the smallest number you must take away from 620 so that it divides exactly by 8?
32. 32.What is the smallest number you must take away from 795 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 9? (a) 3526 (b) 1815 (c) 7812 (d) 2045
34. 34.What is the smallest number you must add to 544 so that it divides exactly by 6?
35. 35.What is the smallest number you must take away from 709 so that it divides exactly by 12?
36. 36.How many factors does 93 have?
37. 37.What is the smallest number you must take away from 459 so that it divides exactly by 4?
38. 38.What is the smallest number you must take away from 124 so that it divides exactly by 9?
39. 39.Which of these numbers divides exactly by 6? (a) 4761 (b) 1740 (c) 5362 (d) 6076
40. 40.Which of these numbers divides exactly by 8? (a) 2027 (b) 7092 (c) 6229 (d) 6352

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