Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 42 · 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.What is the smallest number you must take away from 131 so that it divides exactly by 7?
2. 2.What is the smallest number you must take away from 513 so that it divides exactly by 4?
3. 3.What is the smallest number you must add to 505 so that it divides exactly by 8?
4. 4.Which of these numbers divides exactly by 6? (a) 2815 (b) 8395 (c) 5644 (d) 8226
5. 5.How many factors does 27 have?
6. 6.How many factors does 75 have?
7. 7.What is the smallest number you must take away from 459 so that it divides exactly by 4?
8. 8.How many factors does 72 have?
9. 9.Which of these numbers divides exactly by 3? (a) 3231 (b) 1028 (c) 2239 (d) 8563
10. 10.How many factors does 29 have?
11. 11.Which of these numbers divides exactly by 11? (a) 9317 (b) 1270 (c) 8326 (d) 3337
12. 12.What is the smallest number you must add to 620 so that it divides exactly by 6?
13. 13.What is the smallest number you must add to 510 so that it divides exactly by 8?
14. 14.Which of these numbers divides exactly by 11? (a) 7548 (b) 8222 (c) 1509 (d) 7854
15. 15.How many factors does 53 have?
16. 16.What is the smallest number you must take away from 599 so that it divides exactly by 7?
17. 17.Which of these numbers divides exactly by 6? (a) 4326 (b) 9761 (c) 7388 (d) 8732
18. 18.Which of these numbers divides exactly by 4? (a) 4678 (b) 7372 (c) 1358 (d) 1091
19. 19.Which of these numbers divides exactly by 9? (a) 4736 (b) 3468 (c) 5994 (d) 6425
20. 20.How many factors does 13 have?
21. 21.Which of these numbers divides exactly by 8? (a) 6302 (b) 4544 (c) 9133 (d) 3021
22. 22.What is the smallest number you must add to 310 so that it divides exactly by 12?
23. 23.Which of these numbers divides exactly by 3? (a) 8428 (b) 7925 (c) 6169 (d) 5103
24. 24.Which of these numbers divides exactly by 3? (a) 7496 (b) 6302 (c) 7617 (d) 5009
25. 25.Which of these numbers divides exactly by 9? (a) 2043 (b) 5447 (c) 2193 (d) 6355
26. 26.Which of these numbers divides exactly by 6? (a) 9045 (b) 1171 (c) 8886 (d) 6506
27. 27.What is the smallest number you must add to 246 so that it divides exactly by 4?
28. 28.How many factors does 46 have?
29. 29.Which of these numbers divides exactly by 4? (a) 2291 (b) 3430 (c) 4226 (d) 1744
30. 30.Which of these numbers divides exactly by 6? (a) 3054 (b) 1087 (c) 7696 (d) 2599
31. 31.How many factors does 52 have?
32. 32.What is the smallest number you must add to 567 so that it divides exactly by 4?
33. 33.What is the smallest number you must take away from 693 so that it divides exactly by 13?
34. 34.How many factors does 90 have?
35. 35.How many factors does 37 have?
36. 36.Which of these numbers divides exactly by 3? (a) 4544 (b) 6376 (c) 9000 (d) 7948
37. 37.How many factors does 44 have?
38. 38.How many factors does 82 have?
39. 39.What is the smallest number you must add to 714 so that it divides exactly by 12?
40. 40.What is the smallest number you must add to 928 so that it divides exactly by 3?

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