Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 40 · 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 4? (a) 5173 (b) 3976 (c) 1565 (d) 6635
2. 2.How many factors does 21 have?
3. 3.How many factors does 78 have?
4. 4.What is the smallest number you must take away from 213 so that it divides exactly by 6?
5. 5.What is the smallest number you must add to 107 so that it divides exactly by 9?
6. 6.What is the smallest number you must add to 689 so that it divides exactly by 4?
7. 7.What is the smallest number you must take away from 481 so that it divides exactly by 6?
8. 8.What is the smallest number you must take away from 663 so that it divides exactly by 9?
9. 9.What is the smallest number you must add to 622 so that it divides exactly by 4?
10. 10.What is the smallest number you must take away from 795 so that it divides exactly by 4?
11. 11.Which of these numbers divides exactly by 11? (a) 1298 (b) 1157 (c) 9778 (d) 7220
12. 12.What is the smallest number you must add to 101 so that it divides exactly by 13?
13. 13.What is the smallest number you must add to 555 so that it divides exactly by 8?
14. 14.Which of these numbers divides exactly by 3? (a) 9398 (b) 1703 (c) 4458 (d) 6361
15. 15.Which of these numbers divides exactly by 3? (a) 7034 (b) 8764 (c) 4964 (d) 3807
16. 16.Which of these numbers divides exactly by 11? (a) 2650 (b) 1914 (c) 6278 (d) 1211
17. 17.Which of these numbers divides exactly by 8? (a) 2966 (b) 3583 (c) 9352 (d) 1996
18. 18.How many factors does 100 have?
19. 19.Which of these numbers divides exactly by 11? (a) 4447 (b) 8568 (c) 3662 (d) 9658
20. 20.How many factors does 47 have?
21. 21.What is the smallest number you must add to 691 so that it divides exactly by 11?
22. 22.What is the smallest number you must add to 406 so that it divides exactly by 3?
23. 23.What is the smallest number you must add to 236 so that it divides exactly by 12?
24. 24.What is the smallest number you must take away from 915 so that it divides exactly by 7?
25. 25.What is the smallest number you must take away from 881 so that it divides exactly by 6?
26. 26.What is the smallest number you must add to 800 so that it divides exactly by 6?
27. 27.Which of these numbers divides exactly by 11? (a) 8546 (b) 4801 (c) 5127 (d) 6952
28. 28.What is the smallest number you must add to 242 so that it divides exactly by 4?
29. 29.How many factors does 90 have?
30. 30.How many factors does 39 have?
31. 31.Which of these numbers divides exactly by 3? (a) 7303 (b) 1918 (c) 9447 (d) 8333
32. 32.Which of these numbers divides exactly by 8? (a) 4219 (b) 7073 (c) 5807 (d) 1736
33. 33.What is the smallest number you must add to 874 so that it divides exactly by 4?
34. 34.What is the smallest number you must take away from 421 so that it divides exactly by 12?
35. 35.Which of these numbers divides exactly by 4? (a) 2612 (b) 9705 (c) 9035 (d) 8990
36. 36.What is the smallest number you must add to 359 so that it divides exactly by 4?
37. 37.What is the smallest number you must add to 237 so that it divides exactly by 9?
38. 38.How many factors does 43 have?
39. 39.What is the smallest number you must add to 167 so that it divides exactly by 6?
40. 40.How many factors does 61 have?

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