Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 140 · 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 80 have?
2. 2.How many factors does 26 have?
3. 3.What is the smallest number you must take away from 996 so that it divides exactly by 8?
4. 4.How many factors does 37 have?
5. 5.How many factors does 66 have?
6. 6.What is the smallest number you must add to 134 so that it divides exactly by 4?
7. 7.How many factors does 68 have?
8. 8.What is the smallest number you must take away from 813 so that it divides exactly by 12?
9. 9.How many factors does 52 have?
10. 10.Which of these numbers divides exactly by 3? (a) 3756 (b) 1099 (c) 2168 (d) 1676
11. 11.Which of these numbers divides exactly by 4? (a) 3821 (b) 1049 (c) 7820 (d) 5939
12. 12.How many factors does 32 have?
13. 13.What is the smallest number you must add to 693 so that it divides exactly by 6?
14. 14.What is the smallest number you must add to 984 so that it divides exactly by 9?
15. 15.What is the smallest number you must take away from 836 so that it divides exactly by 13?
16. 16.What is the smallest number you must add to 334 so that it divides exactly by 7?
17. 17.Which of these numbers divides exactly by 6? (a) 9473 (b) 5591 (c) 2442 (d) 8221
18. 18.What is the smallest number you must add to 243 so that it divides exactly by 12?
19. 19.How many factors does 24 have?
20. 20.How many factors does 20 have?
21. 21.Which of these numbers divides exactly by 4? (a) 3773 (b) 9888 (c) 5754 (d) 6978
22. 22.Which of these numbers divides exactly by 6? (a) 4273 (b) 5756 (c) 3449 (d) 1182
23. 23.How many factors does 88 have?
24. 24.What is the smallest number you must take away from 482 so that it divides exactly by 3?
25. 25.What is the smallest number you must take away from 107 so that it divides exactly by 3?
26. 26.What is the smallest number you must take away from 449 so that it divides exactly by 8?
27. 27.Which of these numbers divides exactly by 8? (a) 8496 (b) 7178 (c) 3492 (d) 6727
28. 28.What is the smallest number you must take away from 717 so that it divides exactly by 4?
29. 29.What is the smallest number you must take away from 802 so that it divides exactly by 3?
30. 30.What is the smallest number you must add to 896 so that it divides exactly by 11?
31. 31.What is the smallest number you must take away from 279 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 873 so that it divides exactly by 7?
33. 33.What is the smallest number you must add to 722 so that it divides exactly by 11?
34. 34.Which of these numbers divides exactly by 11? (a) 8074 (b) 4830 (c) 8269 (d) 6942
35. 35.What is the smallest number you must take away from 320 so that it divides exactly by 3?
36. 36.What is the smallest number you must take away from 724 so that it divides exactly by 3?
37. 37.What is the smallest number you must add to 197 so that it divides exactly by 7?
38. 38.Which of these numbers divides exactly by 8? (a) 5418 (b) 6939 (c) 6000 (d) 1226
39. 39.How many factors does 21 have?
40. 40.Which of these numbers divides exactly by 8? (a) 4607 (b) 3089 (c) 1292 (d) 2880

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