Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 147 · 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 23 have?
2. 2.What is the smallest number you must add to 344 so that it divides exactly by 12?
3. 3.What is the smallest number you must add to 450 so that it divides exactly by 7?
4. 4.Which of these numbers divides exactly by 11? (a) 3290 (b) 9955 (c) 3991 (d) 4541
5. 5.Which of these numbers divides exactly by 6? (a) 5448 (b) 1166 (c) 6226 (d) 3596
6. 6.What is the smallest number you must take away from 305 so that it divides exactly by 3?
7. 7.What is the smallest number you must take away from 859 so that it divides exactly by 6?
8. 8.How many factors does 25 have?
9. 9.Which of these numbers divides exactly by 11? (a) 9978 (b) 4154 (c) 6425 (d) 1936
10. 10.How many factors does 45 have?
11. 11.What is the smallest number you must add to 268 so that it divides exactly by 6?
12. 12.What is the smallest number you must take away from 323 so that it divides exactly by 11?
13. 13.Which of these numbers divides exactly by 9? (a) 2529 (b) 3487 (c) 8353 (d) 4173
14. 14.What is the smallest number you must add to 445 so that it divides exactly by 9?
15. 15.What is the smallest number you must take away from 686 so that it divides exactly by 9?
16. 16.How many factors does 44 have?
17. 17.How many factors does 18 have?
18. 18.Which of these numbers divides exactly by 4? (a) 1286 (b) 4097 (c) 8348 (d) 7891
19. 19.How many factors does 30 have?
20. 20.How many factors does 99 have?
21. 21.How many factors does 15 have?
22. 22.How many factors does 92 have?
23. 23.What is the smallest number you must add to 894 so that it divides exactly by 4?
24. 24.What is the smallest number you must take away from 591 so that it divides exactly by 4?
25. 25.What is the smallest number you must take away from 605 so that it divides exactly by 8?
26. 26.What is the smallest number you must take away from 958 so that it divides exactly by 6?
27. 27.Which of these numbers divides exactly by 9? (a) 1155 (b) 8280 (c) 6776 (d) 6789
28. 28.What is the smallest number you must take away from 354 so that it divides exactly by 8?
29. 29.What is the smallest number you must add to 306 so that it divides exactly by 7?
30. 30.What is the smallest number you must add to 919 so that it divides exactly by 7?
31. 31.How many factors does 64 have?
32. 32.How many factors does 87 have?
33. 33.What is the smallest number you must take away from 844 so that it divides exactly by 13?
34. 34.How many factors does 62 have?
35. 35.What is the smallest number you must take away from 479 so that it divides exactly by 3?
36. 36.What is the smallest number you must take away from 270 so that it divides exactly by 11?
37. 37.What is the smallest number you must add to 734 so that it divides exactly by 3?
38. 38.What is the smallest number you must add to 293 so that it divides exactly by 13?
39. 39.What is the smallest number you must add to 789 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 102 so that it divides exactly by 11?

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