Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 59 · 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 8? (a) 2802 (b) 6016 (c) 5802 (d) 3118
2. 2.How many factors does 66 have?
3. 3.What is the smallest number you must take away from 265 so that it divides exactly by 3?
4. 4.How many factors does 21 have?
5. 5.What is the smallest number you must take away from 314 so that it divides exactly by 12?
6. 6.How many factors does 44 have?
7. 7.What is the smallest number you must add to 225 so that it divides exactly by 6?
8. 8.What is the smallest number you must add to 666 so that it divides exactly by 13?
9. 9.How many factors does 38 have?
10. 10.What is the smallest number you must take away from 164 so that it divides exactly by 7?
11. 11.What is the smallest number you must add to 162 so that it divides exactly by 7?
12. 12.Which of these numbers divides exactly by 6? (a) 4836 (b) 3646 (c) 2522 (d) 6134
13. 13.What is the smallest number you must add to 557 so that it divides exactly by 8?
14. 14.Which of these numbers divides exactly by 9? (a) 9777 (b) 7722 (c) 3660 (d) 1745
15. 15.What is the smallest number you must add to 328 so that it divides exactly by 13?
16. 16.Which of these numbers divides exactly by 8? (a) 6474 (b) 5488 (c) 5521 (d) 7215
17. 17.What is the smallest number you must take away from 297 so that it divides exactly by 4?
18. 18.How many factors does 32 have?
19. 19.How many factors does 72 have?
20. 20.What is the smallest number you must add to 554 so that it divides exactly by 6?
21. 21.What is the smallest number you must take away from 286 so that it divides exactly by 3?
22. 22.Which of these numbers divides exactly by 9? (a) 1551 (b) 8720 (c) 9194 (d) 4761
23. 23.What is the smallest number you must take away from 293 so that it divides exactly by 7?
24. 24.What is the smallest number you must add to 535 so that it divides exactly by 12?
25. 25.What is the smallest number you must take away from 510 so that it divides exactly by 9?
26. 26.Which of these numbers divides exactly by 3? (a) 8080 (b) 5177 (c) 3481 (d) 1905
27. 27.Which of these numbers divides exactly by 6? (a) 4653 (b) 8343 (c) 7823 (d) 9690
28. 28.What is the smallest number you must add to 142 so that it divides exactly by 4?
29. 29.How many factors does 12 have?
30. 30.How many factors does 46 have?
31. 31.What is the smallest number you must add to 885 so that it divides exactly by 6?
32. 32.How many factors does 73 have?
33. 33.Which of these numbers divides exactly by 9? (a) 3705 (b) 5054 (c) 7136 (d) 5706
34. 34.Which of these numbers divides exactly by 4? (a) 6142 (b) 6515 (c) 4672 (d) 8967
35. 35.What is the smallest number you must add to 614 so that it divides exactly by 6?
36. 36.What is the smallest number you must take away from 613 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 413 so that it divides exactly by 4?
38. 38.Which of these numbers divides exactly by 6? (a) 7336 (b) 7638 (c) 4307 (d) 5236
39. 39.What is the smallest number you must add to 176 so that it divides exactly by 6?
40. 40.How many factors does 28 have?

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