Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 185 · 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 74 have?
2. 2.What is the smallest number you must take away from 319 so that it divides exactly by 9?
3. 3.What is the smallest number you must take away from 829 so that it divides exactly by 6?
4. 4.What is the smallest number you must take away from 419 so that it divides exactly by 9?
5. 5.How many factors does 92 have?
6. 6.How many factors does 20 have?
7. 7.What is the smallest number you must add to 146 so that it divides exactly by 9?
8. 8.How many factors does 14 have?
9. 9.What is the smallest number you must add to 586 so that it divides exactly by 11?
10. 10.How many factors does 56 have?
11. 11.How many factors does 85 have?
12. 12.Which of these numbers divides exactly by 3? (a) 1052 (b) 4994 (c) 8266 (d) 4002
13. 13.What is the smallest number you must take away from 299 so that it divides exactly by 7?
14. 14.Which of these numbers divides exactly by 6? (a) 5113 (b) 3160 (c) 6660 (d) 4376
15. 15.What is the smallest number you must add to 875 so that it divides exactly by 3?
16. 16.What is the smallest number you must add to 149 so that it divides exactly by 8?
17. 17.How many factors does 39 have?
18. 18.Which of these numbers divides exactly by 6? (a) 4098 (b) 7887 (c) 3941 (d) 8087
19. 19.What is the smallest number you must add to 857 so that it divides exactly by 9?
20. 20.What is the smallest number you must add to 747 so that it divides exactly by 13?
21. 21.What is the smallest number you must add to 293 so that it divides exactly by 13?
22. 22.How many factors does 100 have?
23. 23.What is the smallest number you must take away from 534 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 940 so that it divides exactly by 7?
25. 25.Which of these numbers divides exactly by 3? (a) 2282 (b) 3472 (c) 5954 (d) 5421
26. 26.What is the smallest number you must add to 601 so that it divides exactly by 8?
27. 27.Which of these numbers divides exactly by 6? (a) 6865 (b) 5015 (c) 8550 (d) 2987
28. 28.What is the smallest number you must take away from 760 so that it divides exactly by 7?
29. 29.Which of these numbers divides exactly by 4? (a) 2509 (b) 4983 (c) 5240 (d) 2993
30. 30.What is the smallest number you must add to 871 so that it divides exactly by 4?
31. 31.What is the smallest number you must take away from 200 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 817 so that it divides exactly by 13?
33. 33.What is the smallest number you must add to 194 so that it divides exactly by 8?
34. 34.How many factors does 68 have?
35. 35.What is the smallest number you must take away from 111 so that it divides exactly by 6?
36. 36.How many factors does 49 have?
37. 37.How many factors does 69 have?
38. 38.What is the smallest number you must take away from 722 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 4? (a) 2745 (b) 7064 (c) 4835 (d) 2658
40. 40.What is the smallest number you must add to 735 so that it divides exactly by 8?

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