Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 130 · 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 3? (a) 6801 (b) 1322 (c) 3638 (d) 1123
2. 2.What is the smallest number you must add to 452 so that it divides exactly by 9?
3. 3.Which of these numbers divides exactly by 11? (a) 9340 (b) 7495 (c) 3377 (d) 1984
4. 4.How many factors does 16 have?
5. 5.What is the smallest number you must add to 757 so that it divides exactly by 11?
6. 6.Which of these numbers divides exactly by 3? (a) 5180 (b) 4820 (c) 4509 (d) 7928
7. 7.How many factors does 43 have?
8. 8.Which of these numbers divides exactly by 4? (a) 5693 (b) 3185 (c) 7143 (d) 9036
9. 9.What is the smallest number you must add to 423 so that it divides exactly by 4?
10. 10.Which of these numbers divides exactly by 11? (a) 4730 (b) 3917 (c) 1541 (d) 8236
11. 11.How many factors does 20 have?
12. 12.How many factors does 53 have?
13. 13.How many factors does 70 have?
14. 14.Which of these numbers divides exactly by 4? (a) 6597 (b) 3111 (c) 5228 (d) 4026
15. 15.Which of these numbers divides exactly by 8? (a) 4615 (b) 2973 (c) 6433 (d) 9992
16. 16.Which of these numbers divides exactly by 3? (a) 3232 (b) 7865 (c) 9567 (d) 4318
17. 17.What is the smallest number you must take away from 169 so that it divides exactly by 7?
18. 18.What is the smallest number you must take away from 400 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 266 so that it divides exactly by 6?
20. 20.Which of these numbers divides exactly by 6? (a) 2361 (b) 9821 (c) 9711 (d) 6342
21. 21.Which of these numbers divides exactly by 3? (a) 4304 (b) 1622 (c) 2516 (d) 9981
22. 22.Which of these numbers divides exactly by 9? (a) 4734 (b) 3725 (c) 4679 (d) 2751
23. 23.What is the smallest number you must take away from 368 so that it divides exactly by 9?
24. 24.Which of these numbers divides exactly by 11? (a) 8148 (b) 3430 (c) 1342 (d) 9442
25. 25.What is the smallest number you must take away from 263 so that it divides exactly by 7?
26. 26.Which of these numbers divides exactly by 9? (a) 4190 (b) 7605 (c) 7304 (d) 5307
27. 27.How many factors does 62 have?
28. 28.How many factors does 83 have?
29. 29.What is the smallest number you must take away from 622 so that it divides exactly by 9?
30. 30.How many factors does 72 have?
31. 31.What is the smallest number you must take away from 742 so that it divides exactly by 11?
32. 32.What is the smallest number you must add to 158 so that it divides exactly by 3?
33. 33.How many factors does 26 have?
34. 34.What is the smallest number you must take away from 475 so that it divides exactly by 4?
35. 35.What is the smallest number you must add to 805 so that it divides exactly by 13?
36. 36.How many factors does 36 have?
37. 37.Which of these numbers divides exactly by 4? (a) 9945 (b) 8972 (c) 8027 (d) 4206
38. 38.What is the smallest number you must add to 588 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 4? (a) 6158 (b) 4832 (c) 8077 (d) 7178
40. 40.What is the smallest number you must add to 865 so that it divides exactly by 13?

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