Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 323 · 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.Which of these numbers divides exactly by 4? (a) 9639 (b) 3407 (c) 3108 (d) 7711
2. 2.How many factors does 31 have?
3. 3.How many factors does 47 have?
4. 4.Which of these numbers divides exactly by 3? (a) 7653 (b) 6851 (c) 9110 (d) 8614
5. 5.What is the smallest number you must take away from 635 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 945 so that it divides exactly by 13?
7. 7.Which of these numbers divides exactly by 11? (a) 2938 (b) 7907 (c) 6941 (d) 9455
8. 8.What is the smallest number you must take away from 653 so that it divides exactly by 12?
9. 9.How many factors does 40 have?
10. 10.What is the smallest number you must take away from 311 so that it divides exactly by 3?
11. 11.How many factors does 80 have?
12. 12.What is the smallest number you must add to 275 so that it divides exactly by 6?
13. 13.How many factors does 44 have?
14. 14.What is the smallest number you must add to 827 so that it divides exactly by 3?
15. 15.What is the smallest number you must add to 782 so that it divides exactly by 3?
16. 16.What is the smallest number you must take away from 950 so that it divides exactly by 4?
17. 17.What is the smallest number you must take away from 325 so that it divides exactly by 7?
18. 18.What is the smallest number you must take away from 689 so that it divides exactly by 4?
19. 19.Which of these numbers divides exactly by 4? (a) 8008 (b) 2061 (c) 1694 (d) 6938
20. 20.How many factors does 22 have?
21. 21.What is the smallest number you must add to 563 so that it divides exactly by 11?
22. 22.Which of these numbers divides exactly by 6? (a) 3119 (b) 4201 (c) 1781 (d) 5598
23. 23.How many factors does 79 have?
24. 24.Which of these numbers divides exactly by 4? (a) 4541 (b) 7758 (c) 1224 (d) 2035
25. 25.What is the smallest number you must add to 586 so that it divides exactly by 6?
26. 26.What is the smallest number you must take away from 128 so that it divides exactly by 6?
27. 27.What is the smallest number you must add to 628 so that it divides exactly by 3?
28. 28.Which of these numbers divides exactly by 8? (a) 1405 (b) 6548 (c) 7408 (d) 1373
29. 29.How many factors does 62 have?
30. 30.What is the smallest number you must add to 370 so that it divides exactly by 12?
31. 31.How many factors does 73 have?
32. 32.What is the smallest number you must take away from 991 so that it divides exactly by 3?
33. 33.Which of these numbers divides exactly by 9? (a) 2149 (b) 6694 (c) 9036 (d) 8661
34. 34.What is the smallest number you must take away from 227 so that it divides exactly by 9?
35. 35.Which of these numbers divides exactly by 9? (a) 9095 (b) 3561 (c) 2887 (d) 9684
36. 36.What is the smallest number you must take away from 761 so that it divides exactly by 4?
37. 37.What is the smallest number you must add to 196 so that it divides exactly by 8?
38. 38.How many factors does 94 have?
39. 39.What is the smallest number you must take away from 228 so that it divides exactly by 7?
40. 40.How many factors does 97 have?

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