Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 254 · 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.What is the smallest number you must take away from 319 so that it divides exactly by 12?
2. 2.How many factors does 94 have?
3. 3.What is the smallest number you must take away from 592 so that it divides exactly by 9?
4. 4.How many factors does 97 have?
5. 5.How many factors does 30 have?
6. 6.What is the smallest number you must take away from 834 so that it divides exactly by 9?
7. 7.Which of these numbers divides exactly by 9? (a) 6276 (b) 8811 (c) 8130 (d) 7061
8. 8.How many factors does 41 have?
9. 9.What is the smallest number you must add to 606 so that it divides exactly by 4?
10. 10.What is the smallest number you must take away from 383 so that it divides exactly by 3?
11. 11.What is the smallest number you must add to 297 so that it divides exactly by 4?
12. 12.What is the smallest number you must take away from 416 so that it divides exactly by 12?
13. 13.How many factors does 46 have?
14. 14.What is the smallest number you must add to 551 so that it divides exactly by 6?
15. 15.How many factors does 22 have?
16. 16.Which of these numbers divides exactly by 9? (a) 2781 (b) 5973 (c) 4397 (d) 2652
17. 17.Which of these numbers divides exactly by 3? (a) 2138 (b) 5398 (c) 1370 (d) 7602
18. 18.How many factors does 89 have?
19. 19.Which of these numbers divides exactly by 9? (a) 5973 (b) 2142 (c) 1262 (d) 2109
20. 20.How many factors does 18 have?
21. 21.Which of these numbers divides exactly by 6? (a) 6397 (b) 5522 (c) 3963 (d) 4860
22. 22.Which of these numbers divides exactly by 9? (a) 2662 (b) 5071 (c) 4469 (d) 7497
23. 23.How many factors does 66 have?
24. 24.What is the smallest number you must take away from 613 so that it divides exactly by 9?
25. 25.What is the smallest number you must add to 236 so that it divides exactly by 13?
26. 26.Which of these numbers divides exactly by 8? (a) 4521 (b) 7733 (c) 5321 (d) 8952
27. 27.Which of these numbers divides exactly by 4? (a) 6103 (b) 3492 (c) 7030 (d) 9466
28. 28.How many factors does 43 have?
29. 29.Which of these numbers divides exactly by 8? (a) 1197 (b) 6096 (c) 8156 (d) 1857
30. 30.How many factors does 14 have?
31. 31.What is the smallest number you must add to 986 so that it divides exactly by 4?
32. 32.Which of these numbers divides exactly by 11? (a) 1831 (b) 7846 (c) 1760 (d) 7578
33. 33.What is the smallest number you must add to 115 so that it divides exactly by 6?
34. 34.What is the smallest number you must take away from 123 so that it divides exactly by 11?
35. 35.Which of these numbers divides exactly by 11? (a) 1240 (b) 9630 (c) 4371 (d) 3729
36. 36.What is the smallest number you must add to 251 so that it divides exactly by 3?
37. 37.What is the smallest number you must add to 151 so that it divides exactly by 6?
38. 38.How many factors does 62 have?
39. 39.What is the smallest number you must add to 229 so that it divides exactly by 12?
40. 40.What is the smallest number you must take away from 699 so that it divides exactly by 7?

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