Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 220 · 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 67 have?
2. 2.Which of these numbers divides exactly by 3? (a) 6814 (b) 5396 (c) 9741 (d) 6817
3. 3.What is the smallest number you must take away from 926 so that it divides exactly by 4?
4. 4.What is the smallest number you must add to 836 so that it divides exactly by 12?
5. 5.How many factors does 18 have?
6. 6.What is the smallest number you must take away from 351 so that it divides exactly by 7?
7. 7.What is the smallest number you must add to 983 so that it divides exactly by 9?
8. 8.What is the smallest number you must add to 993 so that it divides exactly by 4?
9. 9.How many factors does 27 have?
10. 10.What is the smallest number you must take away from 905 so that it divides exactly by 11?
11. 11.What is the smallest number you must add to 256 so that it divides exactly by 6?
12. 12.How many factors does 40 have?
13. 13.What is the smallest number you must take away from 964 so that it divides exactly by 13?
14. 14.What is the smallest number you must take away from 398 so that it divides exactly by 12?
15. 15.Which of these numbers divides exactly by 6? (a) 3407 (b) 1908 (c) 4310 (d) 4617
16. 16.What is the smallest number you must add to 297 so that it divides exactly by 12?
17. 17.Which of these numbers divides exactly by 6? (a) 7160 (b) 5867 (c) 7415 (d) 4746
18. 18.What is the smallest number you must take away from 283 so that it divides exactly by 6?
19. 19.Which of these numbers divides exactly by 11? (a) 5417 (b) 8976 (c) 2504 (d) 9765
20. 20.How many factors does 72 have?
21. 21.How many factors does 21 have?
22. 22.What is the smallest number you must take away from 231 so that it divides exactly by 13?
23. 23.What is the smallest number you must take away from 214 so that it divides exactly by 13?
24. 24.Which of these numbers divides exactly by 11? (a) 4862 (b) 3385 (c) 2661 (d) 3472
25. 25.Which of these numbers divides exactly by 4? (a) 7985 (b) 9796 (c) 2114 (d) 3190
26. 26.Which of these numbers divides exactly by 6? (a) 4568 (b) 8115 (c) 8612 (d) 3816
27. 27.What is the smallest number you must add to 926 so that it divides exactly by 8?
28. 28.What is the smallest number you must take away from 744 so that it divides exactly by 13?
29. 29.What is the smallest number you must add to 560 so that it divides exactly by 11?
30. 30.Which of these numbers divides exactly by 4? (a) 3998 (b) 6159 (c) 2468 (d) 3110
31. 31.How many factors does 37 have?
32. 32.What is the smallest number you must add to 322 so that it divides exactly by 11?
33. 33.How many factors does 56 have?
34. 34.What is the smallest number you must add to 214 so that it divides exactly by 8?
35. 35.Which of these numbers divides exactly by 6? (a) 9263 (b) 7668 (c) 9782 (d) 1936
36. 36.What is the smallest number you must take away from 107 so that it divides exactly by 7?
37. 37.What is the smallest number you must take away from 328 so that it divides exactly by 3?
38. 38.What is the smallest number you must take away from 803 so that it divides exactly by 12?
39. 39.How many factors does 91 have?
40. 40.What is the smallest number you must add to 977 so that it divides exactly by 7?

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