Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 153 · 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 97 have?
2. 2.How many factors does 91 have?
3. 3.What is the smallest number you must take away from 657 so that it divides exactly by 7?
4. 4.What is the smallest number you must add to 417 so that it divides exactly by 9?
5. 5.Which of these numbers divides exactly by 3? (a) 5629 (b) 8407 (c) 4150 (d) 1659
6. 6.What is the smallest number you must add to 240 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 376 so that it divides exactly by 12?
8. 8.What is the smallest number you must take away from 491 so that it divides exactly by 7?
9. 9.How many factors does 54 have?
10. 10.How many factors does 33 have?
11. 11.How many factors does 13 have?
12. 12.What is the smallest number you must add to 837 so that it divides exactly by 13?
13. 13.Which of these numbers divides exactly by 6? (a) 4284 (b) 6025 (c) 9304 (d) 4227
14. 14.What is the smallest number you must add to 236 so that it divides exactly by 7?
15. 15.What is the smallest number you must take away from 959 so that it divides exactly by 3?
16. 16.How many factors does 84 have?
17. 17.Which of these numbers divides exactly by 11? (a) 1408 (b) 8818 (c) 4486 (d) 9532
18. 18.How many factors does 21 have?
19. 19.What is the smallest number you must take away from 391 so that it divides exactly by 11?
20. 20.How many factors does 79 have?
21. 21.How many factors does 55 have?
22. 22.Which of these numbers divides exactly by 8? (a) 8250 (b) 4241 (c) 8872 (d) 3686
23. 23.Which of these numbers divides exactly by 4? (a) 1635 (b) 1512 (c) 2995 (d) 3653
24. 24.What is the smallest number you must add to 711 so that it divides exactly by 6?
25. 25.How many factors does 40 have?
26. 26.What is the smallest number you must take away from 174 so that it divides exactly by 4?
27. 27.What is the smallest number you must add to 881 so that it divides exactly by 9?
28. 28.Which of these numbers divides exactly by 3? (a) 8416 (b) 6475 (c) 4528 (d) 1956
29. 29.What is the smallest number you must take away from 472 so that it divides exactly by 9?
30. 30.What is the smallest number you must add to 973 so that it divides exactly by 4?
31. 31.What is the smallest number you must add to 778 so that it divides exactly by 4?
32. 32.What is the smallest number you must add to 518 so that it divides exactly by 13?
33. 33.What is the smallest number you must add to 818 so that it divides exactly by 7?
34. 34.How many factors does 12 have?
35. 35.Which of these numbers divides exactly by 4? (a) 5744 (b) 8709 (c) 2955 (d) 2931
36. 36.Which of these numbers divides exactly by 6? (a) 6682 (b) 1219 (c) 2785 (d) 8610
37. 37.What is the smallest number you must take away from 621 so that it divides exactly by 13?
38. 38.What is the smallest number you must take away from 643 so that it divides exactly by 8?
39. 39.Which of these numbers divides exactly by 6? (a) 3634 (b) 3887 (c) 8635 (d) 9198
40. 40.What is the smallest number you must add to 263 so that it divides exactly by 9?

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