Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 317 · 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 56 have?
2. 2.What is the smallest number you must take away from 970 so that it divides exactly by 8?
3. 3.Which of these numbers divides exactly by 9? (a) 9252 (b) 1519 (c) 1938 (d) 3981
4. 4.Which of these numbers divides exactly by 6? (a) 3303 (b) 4839 (c) 8122 (d) 2520
5. 5.What is the smallest number you must take away from 122 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 352 so that it divides exactly by 13?
7. 7.What is the smallest number you must add to 469 so that it divides exactly by 12?
8. 8.Which of these numbers divides exactly by 8? (a) 1064 (b) 6446 (c) 5037 (d) 2898
9. 9.How many factors does 53 have?
10. 10.How many factors does 88 have?
11. 11.Which of these numbers divides exactly by 3? (a) 3092 (b) 7134 (c) 3439 (d) 1834
12. 12.What is the smallest number you must take away from 531 so that it divides exactly by 6?
13. 13.What is the smallest number you must take away from 944 so that it divides exactly by 6?
14. 14.How many factors does 87 have?
15. 15.Which of these numbers divides exactly by 9? (a) 6640 (b) 3814 (c) 3663 (d) 1520
16. 16.How many factors does 37 have?
17. 17.What is the smallest number you must take away from 565 so that it divides exactly by 4?
18. 18.How many factors does 64 have?
19. 19.What is the smallest number you must take away from 248 so that it divides exactly by 9?
20. 20.How many factors does 18 have?
21. 21.What is the smallest number you must take away from 641 so that it divides exactly by 8?
22. 22.How many factors does 63 have?
23. 23.How many factors does 42 have?
24. 24.How many factors does 100 have?
25. 25.What is the smallest number you must add to 978 so that it divides exactly by 13?
26. 26.Which of these numbers divides exactly by 8? (a) 5808 (b) 6988 (c) 8334 (d) 1903
27. 27.Which of these numbers divides exactly by 3? (a) 9407 (b) 1632 (c) 4505 (d) 1423
28. 28.Which of these numbers divides exactly by 6? (a) 5677 (b) 8564 (c) 2035 (d) 7170
29. 29.How many factors does 69 have?
30. 30.What is the smallest number you must take away from 466 so that it divides exactly by 3?
31. 31.What is the smallest number you must add to 557 so that it divides exactly by 9?
32. 32.What is the smallest number you must take away from 800 so that it divides exactly by 12?
33. 33.How many factors does 46 have?
34. 34.What is the smallest number you must take away from 847 so that it divides exactly by 9?
35. 35.What is the smallest number you must add to 742 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 453 so that it divides exactly by 4?
37. 37.Which of these numbers divides exactly by 8? (a) 2448 (b) 6655 (c) 1441 (d) 2183
38. 38.Which of these numbers divides exactly by 6? (a) 2661 (b) 4034 (c) 6288 (d) 3531
39. 39.What is the smallest number you must take away from 983 so that it divides exactly by 7?
40. 40.Which of these numbers divides exactly by 11? (a) 2107 (b) 6960 (c) 7330 (d) 5489

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