Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 79 · 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 422 so that it divides exactly by 12?
2. 2.Which of these numbers divides exactly by 9? (a) 5724 (b) 9359 (c) 7699 (d) 5682
3. 3.Which of these numbers divides exactly by 9? (a) 4944 (b) 1726 (c) 7392 (d) 2466
4. 4.What is the smallest number you must take away from 210 so that it divides exactly by 9?
5. 5.What is the smallest number you must add to 293 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 505 so that it divides exactly by 3?
7. 7.Which of these numbers divides exactly by 11? (a) 6685 (b) 5879 (c) 2494 (d) 3707
8. 8.How many factors does 76 have?
9. 9.What is the smallest number you must take away from 639 so that it divides exactly by 8?
10. 10.What is the smallest number you must add to 302 so that it divides exactly by 3?
11. 11.Which of these numbers divides exactly by 3? (a) 5489 (b) 5878 (c) 3037 (d) 1137
12. 12.What is the smallest number you must take away from 406 so that it divides exactly by 3?
13. 13.What is the smallest number you must take away from 941 so that it divides exactly by 8?
14. 14.How many factors does 51 have?
15. 15.What is the smallest number you must take away from 905 so that it divides exactly by 7?
16. 16.What is the smallest number you must add to 190 so that it divides exactly by 6?
17. 17.Which of these numbers divides exactly by 11? (a) 2640 (b) 8766 (c) 2274 (d) 2732
18. 18.What is the smallest number you must add to 277 so that it divides exactly by 13?
19. 19.How many factors does 50 have?
20. 20.How many factors does 74 have?
21. 21.Which of these numbers divides exactly by 3? (a) 2347 (b) 8061 (c) 7856 (d) 7918
22. 22.How many factors does 89 have?
23. 23.Which of these numbers divides exactly by 6? (a) 4171 (b) 5230 (c) 2286 (d) 8931
24. 24.How many factors does 38 have?
25. 25.What is the smallest number you must add to 409 so that it divides exactly by 6?
26. 26.How many factors does 54 have?
27. 27.Which of these numbers divides exactly by 4? (a) 8193 (b) 9983 (c) 3656 (d) 1025
28. 28.What is the smallest number you must take away from 967 so that it divides exactly by 6?
29. 29.What is the smallest number you must add to 540 so that it divides exactly by 8?
30. 30.What is the smallest number you must add to 291 so that it divides exactly by 6?
31. 31.Which of these numbers divides exactly by 3? (a) 2840 (b) 5024 (c) 1979 (d) 3606
32. 32.Which of these numbers divides exactly by 8? (a) 4720 (b) 8197 (c) 3389 (d) 6393
33. 33.What is the smallest number you must add to 470 so that it divides exactly by 7?
34. 34.Which of these numbers divides exactly by 4? (a) 5813 (b) 8877 (c) 3195 (d) 9564
35. 35.What is the smallest number you must take away from 229 so that it divides exactly by 8?
36. 36.What is the smallest number you must take away from 787 so that it divides exactly by 7?
37. 37.What is the smallest number you must add to 385 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 374 so that it divides exactly by 8?
39. 39.Which of these numbers divides exactly by 4? (a) 3278 (b) 3695 (c) 4244 (d) 2771
40. 40.Which of these numbers divides exactly by 9? (a) 7687 (b) 1008 (c) 3086 (d) 3903

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