Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 103 · 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 add to 942 so that it divides exactly by 7?
2. 2.Which of these numbers divides exactly by 11? (a) 9936 (b) 8217 (c) 1553 (d) 2944
3. 3.Which of these numbers divides exactly by 6? (a) 8106 (b) 8212 (c) 4903 (d) 9573
4. 4.How many factors does 12 have?
5. 5.Which of these numbers divides exactly by 8? (a) 1170 (b) 4456 (c) 8594 (d) 7218
6. 6.Which of these numbers divides exactly by 11? (a) 6167 (b) 4065 (c) 4779 (d) 1892
7. 7.What is the smallest number you must add to 189 so that it divides exactly by 6?
8. 8.What is the smallest number you must take away from 195 so that it divides exactly by 7?
9. 9.How many factors does 85 have?
10. 10.What is the smallest number you must add to 988 so that it divides exactly by 3?
11. 11.Which of these numbers divides exactly by 11? (a) 9922 (b) 9826 (c) 6810 (d) 7747
12. 12.What is the smallest number you must take away from 989 so that it divides exactly by 7?
13. 13.What is the smallest number you must take away from 536 so that it divides exactly by 13?
14. 14.Which of these numbers divides exactly by 3? (a) 1097 (b) 2380 (c) 5522 (d) 2379
15. 15.How many factors does 31 have?
16. 16.How many factors does 49 have?
17. 17.How many factors does 35 have?
18. 18.What is the smallest number you must take away from 999 so that it divides exactly by 4?
19. 19.How many factors does 70 have?
20. 20.What is the smallest number you must add to 419 so that it divides exactly by 8?
21. 21.What is the smallest number you must add to 186 so that it divides exactly by 9?
22. 22.What is the smallest number you must add to 580 so that it divides exactly by 12?
23. 23.Which of these numbers divides exactly by 6? (a) 9703 (b) 1770 (c) 3776 (d) 7053
24. 24.What is the smallest number you must take away from 856 so that it divides exactly by 3?
25. 25.How many factors does 91 have?
26. 26.How many factors does 40 have?
27. 27.How many factors does 26 have?
28. 28.What is the smallest number you must add to 803 so that it divides exactly by 3?
29. 29.What is the smallest number you must add to 128 so that it divides exactly by 9?
30. 30.What is the smallest number you must take away from 379 so that it divides exactly by 12?
31. 31.Which of these numbers divides exactly by 3? (a) 8499 (b) 8525 (c) 6193 (d) 7711
32. 32.What is the smallest number you must add to 626 so that it divides exactly by 11?
33. 33.Which of these numbers divides exactly by 3? (a) 6700 (b) 5178 (c) 6829 (d) 8200
34. 34.What is the smallest number you must take away from 436 so that it divides exactly by 3?
35. 35.What is the smallest number you must take away from 721 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 817 so that it divides exactly by 4?
37. 37.Which of these numbers divides exactly by 4? (a) 9488 (b) 8773 (c) 7094 (d) 6581
38. 38.Which of these numbers divides exactly by 4? (a) 1500 (b) 8795 (c) 9447 (d) 9138
39. 39.What is the smallest number you must take away from 428 so that it divides exactly by 11?
40. 40.What is the smallest number you must add to 376 so that it divides exactly by 12?

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