Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 307 · 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 22 have?
2. 2.What is the smallest number you must add to 862 so that it divides exactly by 4?
3. 3.What is the smallest number you must take away from 460 so that it divides exactly by 6?
4. 4.How many factors does 17 have?
5. 5.Which of these numbers divides exactly by 6? (a) 6161 (b) 1340 (c) 4416 (d) 1504
6. 6.Which of these numbers divides exactly by 3? (a) 6124 (b) 1726 (c) 7758 (d) 5834
7. 7.What is the smallest number you must add to 415 so that it divides exactly by 4?
8. 8.Which of these numbers divides exactly by 11? (a) 4631 (b) 6835 (c) 3342 (d) 6178
9. 9.What is the smallest number you must add to 427 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 815 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 709 so that it divides exactly by 11?
12. 12.What is the smallest number you must take away from 415 so that it divides exactly by 7?
13. 13.How many factors does 23 have?
14. 14.Which of these numbers divides exactly by 9? (a) 3826 (b) 8222 (c) 5654 (d) 3618
15. 15.What is the smallest number you must take away from 223 so that it divides exactly by 7?
16. 16.What is the smallest number you must add to 335 so that it divides exactly by 3?
17. 17.How many factors does 31 have?
18. 18.How many factors does 91 have?
19. 19.Which of these numbers divides exactly by 4? (a) 9191 (b) 9202 (c) 6961 (d) 9952
20. 20.What is the smallest number you must add to 640 so that it divides exactly by 6?
21. 21.Which of these numbers divides exactly by 8? (a) 3656 (b) 4255 (c) 9398 (d) 5572
22. 22.Which of these numbers divides exactly by 9? (a) 3987 (b) 5443 (c) 3189 (d) 8027
23. 23.Which of these numbers divides exactly by 6? (a) 3994 (b) 1141 (c) 7986 (d) 5099
24. 24.What is the smallest number you must add to 955 so that it divides exactly by 7?
25. 25.How many factors does 55 have?
26. 26.What is the smallest number you must add to 954 so that it divides exactly by 12?
27. 27.How many factors does 21 have?
28. 28.What is the smallest number you must add to 859 so that it divides exactly by 3?
29. 29.What is the smallest number you must add to 364 so that it divides exactly by 12?
30. 30.What is the smallest number you must add to 191 so that it divides exactly by 4?
31. 31.How many factors does 46 have?
32. 32.What is the smallest number you must add to 582 so that it divides exactly by 12?
33. 33.How many factors does 83 have?
34. 34.How many factors does 51 have?
35. 35.What is the smallest number you must add to 327 so that it divides exactly by 6?
36. 36.What is the smallest number you must take away from 799 so that it divides exactly by 7?
37. 37.What is the smallest number you must take away from 567 so that it divides exactly by 4?
38. 38.What is the smallest number you must take away from 821 so that it divides exactly by 6?
39. 39.What is the smallest number you must take away from 113 so that it divides exactly by 3?
40. 40.What is the smallest number you must add to 496 so that it divides exactly by 3?

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