Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 332 · 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.Which of these numbers divides exactly by 11? (a) 6182 (b) 3595 (c) 6529 (d) 3510
2. 2.How many factors does 41 have?
3. 3.How many factors does 91 have?
4. 4.What is the smallest number you must add to 130 so that it divides exactly by 11?
5. 5.How many factors does 17 have?
6. 6.What is the smallest number you must add to 626 so that it divides exactly by 7?
7. 7.What is the smallest number you must add to 391 so that it divides exactly by 9?
8. 8.How many factors does 49 have?
9. 9.What is the smallest number you must add to 394 so that it divides exactly by 12?
10. 10.Which of these numbers divides exactly by 4? (a) 7034 (b) 7592 (c) 4865 (d) 3433
11. 11.What is the smallest number you must add to 284 so that it divides exactly by 9?
12. 12.What is the smallest number you must add to 585 so that it divides exactly by 8?
13. 13.What is the smallest number you must add to 830 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 703 so that it divides exactly by 3?
15. 15.What is the smallest number you must add to 399 so that it divides exactly by 4?
16. 16.Which of these numbers divides exactly by 8? (a) 8619 (b) 8101 (c) 5063 (d) 5792
17. 17.How many factors does 16 have?
18. 18.What is the smallest number you must add to 273 so that it divides exactly by 11?
19. 19.How many factors does 87 have?
20. 20.Which of these numbers divides exactly by 4? (a) 4894 (b) 8569 (c) 2665 (d) 9240
21. 21.What is the smallest number you must add to 203 so that it divides exactly by 8?
22. 22.How many factors does 60 have?
23. 23.How many factors does 24 have?
24. 24.How many factors does 98 have?
25. 25.What is the smallest number you must take away from 164 so that it divides exactly by 13?
26. 26.What is the smallest number you must take away from 480 so that it divides exactly by 7?
27. 27.What is the smallest number you must add to 475 so that it divides exactly by 4?
28. 28.What is the smallest number you must take away from 161 so that it divides exactly by 8?
29. 29.What is the smallest number you must add to 842 so that it divides exactly by 3?
30. 30.How many factors does 92 have?
31. 31.Which of these numbers divides exactly by 3? (a) 4372 (b) 3669 (c) 3872 (d) 6253
32. 32.What is the smallest number you must add to 607 so that it divides exactly by 4?
33. 33.What is the smallest number you must add to 593 so that it divides exactly by 12?
34. 34.What is the smallest number you must take away from 945 so that it divides exactly by 12?
35. 35.What is the smallest number you must take away from 680 so that it divides exactly by 13?
36. 36.What is the smallest number you must take away from 415 so that it divides exactly by 4?
37. 37.What is the smallest number you must add to 113 so that it divides exactly by 12?
38. 38.Which of these numbers divides exactly by 8? (a) 3722 (b) 1592 (c) 1613 (d) 2202
39. 39.What is the smallest number you must add to 205 so that it divides exactly by 6?
40. 40.How many factors does 12 have?

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