Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 328 · 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 87 have?
2. 2.What is the smallest number you must add to 282 so that it divides exactly by 12?
3. 3.What is the smallest number you must take away from 488 so that it divides exactly by 9?
4. 4.What is the smallest number you must add to 611 so that it divides exactly by 9?
5. 5.How many factors does 33 have?
6. 6.What is the smallest number you must take away from 862 so that it divides exactly by 12?
7. 7.How many factors does 27 have?
8. 8.How many factors does 63 have?
9. 9.Which of these numbers divides exactly by 3? (a) 6094 (b) 2267 (c) 8942 (d) 9273
10. 10.What is the smallest number you must take away from 830 so that it divides exactly by 11?
11. 11.What is the smallest number you must add to 785 so that it divides exactly by 13?
12. 12.What is the smallest number you must add to 148 so that it divides exactly by 6?
13. 13.What is the smallest number you must add to 146 so that it divides exactly by 3?
14. 14.Which of these numbers divides exactly by 11? (a) 7337 (b) 1715 (c) 2352 (d) 2560
15. 15.Which of these numbers divides exactly by 9? (a) 6639 (b) 7767 (c) 3979 (d) 7940
16. 16.What is the smallest number you must add to 857 so that it divides exactly by 4?
17. 17.What is the smallest number you must take away from 153 so that it divides exactly by 13?
18. 18.How many factors does 85 have?
19. 19.How many factors does 40 have?
20. 20.What is the smallest number you must take away from 134 so that it divides exactly by 3?
21. 21.What is the smallest number you must take away from 717 so that it divides exactly by 13?
22. 22.Which of these numbers divides exactly by 3? (a) 9510 (b) 6649 (c) 6103 (d) 2305
23. 23.Which of these numbers divides exactly by 3? (a) 6243 (b) 5788 (c) 8212 (d) 6232
24. 24.What is the smallest number you must take away from 354 so that it divides exactly by 4?
25. 25.Which of these numbers divides exactly by 4? (a) 4452 (b) 3125 (c) 6079 (d) 4963
26. 26.Which of these numbers divides exactly by 6? (a) 2682 (b) 2899 (c) 2271 (d) 3523
27. 27.How many factors does 32 have?
28. 28.What is the smallest number you must add to 222 so that it divides exactly by 13?
29. 29.What is the smallest number you must take away from 474 so that it divides exactly by 13?
30. 30.Which of these numbers divides exactly by 3? (a) 4172 (b) 7856 (c) 6514 (d) 7437
31. 31.Which of these numbers divides exactly by 11? (a) 6241 (b) 8256 (c) 1452 (d) 6338
32. 32.Which of these numbers divides exactly by 9? (a) 3690 (b) 2758 (c) 2751 (d) 9727
33. 33.What is the smallest number you must take away from 571 so that it divides exactly by 13?
34. 34.What is the smallest number you must add to 335 so that it divides exactly by 11?
35. 35.Which of these numbers divides exactly by 11? (a) 8735 (b) 4352 (c) 1512 (d) 5775
36. 36.How many factors does 65 have?
37. 37.Which of these numbers divides exactly by 4? (a) 2173 (b) 4673 (c) 1548 (d) 9222
38. 38.How many factors does 23 have?
39. 39.What is the smallest number you must add to 361 so that it divides exactly by 13?
40. 40.What is the smallest number you must add to 980 so that it divides exactly by 11?

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