Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 175 · 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 79 have?
2. 2.How many factors does 15 have?
3. 3.What is the smallest number you must add to 862 so that it divides exactly by 11?
4. 4.What is the smallest number you must take away from 639 so that it divides exactly by 4?
5. 5.What is the smallest number you must take away from 766 so that it divides exactly by 6?
6. 6.What is the smallest number you must take away from 343 so that it divides exactly by 6?
7. 7.Which of these numbers divides exactly by 8? (a) 2779 (b) 9482 (c) 4545 (d) 8392
8. 8.How many factors does 69 have?
9. 9.Which of these numbers divides exactly by 3? (a) 4039 (b) 5523 (c) 5332 (d) 4192
10. 10.How many factors does 85 have?
11. 11.Which of these numbers divides exactly by 8? (a) 2307 (b) 3308 (c) 8672 (d) 7217
12. 12.How many factors does 49 have?
13. 13.What is the smallest number you must add to 573 so that it divides exactly by 7?
14. 14.What is the smallest number you must add to 152 so that it divides exactly by 6?
15. 15.Which of these numbers divides exactly by 4? (a) 4943 (b) 8276 (c) 1045 (d) 7829
16. 16.Which of these numbers divides exactly by 6? (a) 4942 (b) 4826 (c) 3391 (d) 7644
17. 17.What is the smallest number you must add to 569 so that it divides exactly by 13?
18. 18.How many factors does 22 have?
19. 19.What is the smallest number you must take away from 716 so that it divides exactly by 6?
20. 20.What is the smallest number you must take away from 778 so that it divides exactly by 3?
21. 21.How many factors does 21 have?
22. 22.What is the smallest number you must take away from 882 so that it divides exactly by 4?
23. 23.What is the smallest number you must take away from 620 so that it divides exactly by 6?
24. 24.Which of these numbers divides exactly by 4? (a) 5609 (b) 5820 (c) 3497 (d) 1581
25. 25.What is the smallest number you must take away from 886 so that it divides exactly by 6?
26. 26.Which of these numbers divides exactly by 4? (a) 2119 (b) 3958 (c) 4592 (d) 1922
27. 27.What is the smallest number you must take away from 515 so that it divides exactly by 12?
28. 28.What is the smallest number you must add to 677 so that it divides exactly by 7?
29. 29.What is the smallest number you must add to 949 so that it divides exactly by 11?
30. 30.What is the smallest number you must add to 497 so that it divides exactly by 11?
31. 31.What is the smallest number you must add to 971 so that it divides exactly by 4?
32. 32.What is the smallest number you must take away from 622 so that it divides exactly by 11?
33. 33.What is the smallest number you must take away from 469 so that it divides exactly by 4?
34. 34.How many factors does 82 have?
35. 35.What is the smallest number you must add to 861 so that it divides exactly by 13?
36. 36.How many factors does 48 have?
37. 37.Which of these numbers divides exactly by 4? (a) 5273 (b) 2548 (c) 3066 (d) 1939
38. 38.Which of these numbers divides exactly by 9? (a) 2968 (b) 1249 (c) 2890 (d) 7641
39. 39.Which of these numbers divides exactly by 4? (a) 5052 (b) 9221 (c) 5229 (d) 6270
40. 40.What is the smallest number you must add to 941 so that it divides exactly by 3?

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