Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 334 · 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 51 have?
2. 2.What is the smallest number you must add to 366 so that it divides exactly by 12?
3. 3.Which of these numbers divides exactly by 8? (a) 6095 (b) 4375 (c) 6552 (d) 3146
4. 4.What is the smallest number you must add to 523 so that it divides exactly by 4?
5. 5.What is the smallest number you must take away from 647 so that it divides exactly by 11?
6. 6.How many factors does 31 have?
7. 7.How many factors does 55 have?
8. 8.How many factors does 43 have?
9. 9.How many factors does 13 have?
10. 10.What is the smallest number you must add to 709 so that it divides exactly by 6?
11. 11.How many factors does 58 have?
12. 12.Which of these numbers divides exactly by 11? (a) 3861 (b) 8287 (c) 3518 (d) 9880
13. 13.What is the smallest number you must take away from 254 so that it divides exactly by 7?
14. 14.Which of these numbers divides exactly by 3? (a) 2675 (b) 6348 (c) 8591 (d) 3730
15. 15.What is the smallest number you must take away from 803 so that it divides exactly by 6?
16. 16.What is the smallest number you must add to 589 so that it divides exactly by 8?
17. 17.Which of these numbers divides exactly by 11? (a) 3465 (b) 1664 (c) 8958 (d) 5210
18. 18.What is the smallest number you must add to 624 so that it divides exactly by 7?
19. 19.What is the smallest number you must take away from 929 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 222 so that it divides exactly by 11?
21. 21.How many factors does 93 have?
22. 22.What is the smallest number you must take away from 834 so that it divides exactly by 9?
23. 23.Which of these numbers divides exactly by 3? (a) 5965 (b) 2808 (c) 9706 (d) 2980
24. 24.What is the smallest number you must add to 334 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 548 so that it divides exactly by 12?
26. 26.Which of these numbers divides exactly by 4? (a) 8253 (b) 4482 (c) 1932 (d) 4765
27. 27.Which of these numbers divides exactly by 8? (a) 8856 (b) 8567 (c) 7841 (d) 1613
28. 28.How many factors does 75 have?
29. 29.How many factors does 15 have?
30. 30.What is the smallest number you must add to 705 so that it divides exactly by 11?
31. 31.Which of these numbers divides exactly by 9? (a) 3261 (b) 3333 (c) 2102 (d) 8712
32. 32.How many factors does 14 have?
33. 33.Which of these numbers divides exactly by 9? (a) 5607 (b) 5142 (c) 5838 (d) 9687
34. 34.What is the smallest number you must take away from 337 so that it divides exactly by 3?
35. 35.What is the smallest number you must take away from 364 so that it divides exactly by 3?
36. 36.What is the smallest number you must take away from 322 so that it divides exactly by 12?
37. 37.How many factors does 24 have?
38. 38.Which of these numbers divides exactly by 8? (a) 4563 (b) 1970 (c) 8773 (d) 3552
39. 39.Which of these numbers divides exactly by 4? (a) 9096 (b) 9039 (c) 9090 (d) 1391
40. 40.How many factors does 86 have?

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