Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 143 · 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 52 have?
2. 2.Which of these numbers divides exactly by 8? (a) 2195 (b) 5214 (c) 2719 (d) 7896
3. 3.What is the smallest number you must take away from 869 so that it divides exactly by 7?
4. 4.How many factors does 24 have?
5. 5.Which of these numbers divides exactly by 4? (a) 1921 (b) 7592 (c) 2418 (d) 9045
6. 6.How many factors does 21 have?
7. 7.Which of these numbers divides exactly by 3? (a) 5683 (b) 9495 (c) 1639 (d) 5254
8. 8.What is the smallest number you must take away from 853 so that it divides exactly by 12?
9. 9.Which of these numbers divides exactly by 8? (a) 1424 (b) 5369 (c) 8101 (d) 8046
10. 10.What is the smallest number you must take away from 469 so that it divides exactly by 6?
11. 11.What is the smallest number you must add to 226 so that it divides exactly by 8?
12. 12.What is the smallest number you must add to 698 so that it divides exactly by 6?
13. 13.How many factors does 57 have?
14. 14.What is the smallest number you must add to 978 so that it divides exactly by 8?
15. 15.Which of these numbers divides exactly by 3? (a) 2784 (b) 6178 (c) 6001 (d) 1472
16. 16.What is the smallest number you must take away from 137 so that it divides exactly by 3?
17. 17.What is the smallest number you must add to 647 so that it divides exactly by 9?
18. 18.What is the smallest number you must add to 443 so that it divides exactly by 9?
19. 19.Which of these numbers divides exactly by 3? (a) 3124 (b) 7495 (c) 8251 (d) 8895
20. 20.What is the smallest number you must take away from 658 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 985 so that it divides exactly by 6?
22. 22.How many factors does 100 have?
23. 23.How many factors does 43 have?
24. 24.What is the smallest number you must take away from 995 so that it divides exactly by 13?
25. 25.What is the smallest number you must take away from 136 so that it divides exactly by 12?
26. 26.Which of these numbers divides exactly by 9? (a) 5931 (b) 1001 (c) 2994 (d) 6953
27. 27.What is the smallest number you must add to 569 so that it divides exactly by 6?
28. 28.How many factors does 67 have?
29. 29.What is the smallest number you must take away from 843 so that it divides exactly by 13?
30. 30.What is the smallest number you must take away from 632 so that it divides exactly by 6?
31. 31.Which of these numbers divides exactly by 6? (a) 3498 (b) 8788 (c) 3050 (d) 7748
32. 32.Which of these numbers divides exactly by 6? (a) 3246 (b) 4763 (c) 6202 (d) 2063
33. 33.What is the smallest number you must add to 707 so that it divides exactly by 4?
34. 34.What is the smallest number you must add to 939 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 288 so that it divides exactly by 7?
36. 36.What is the smallest number you must add to 849 so that it divides exactly by 9?
37. 37.What is the smallest number you must add to 649 so that it divides exactly by 3?
38. 38.How many factors does 25 have?
39. 39.What is the smallest number you must take away from 969 so that it divides exactly by 6?
40. 40.What is the smallest number you must take away from 401 so that it divides exactly by 7?

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