Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 151 · 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 20 have?
2. 2.Which of these numbers divides exactly by 9? (a) 4211 (b) 4669 (c) 2413 (d) 1368
3. 3.Which of these numbers divides exactly by 11? (a) 1410 (b) 3861 (c) 8292 (d) 6348
4. 4.What is the smallest number you must add to 274 so that it divides exactly by 3?
5. 5.What is the smallest number you must add to 340 so that it divides exactly by 11?
6. 6.What is the smallest number you must add to 326 so that it divides exactly by 9?
7. 7.What is the smallest number you must add to 297 so that it divides exactly by 6?
8. 8.How many factors does 53 have?
9. 9.Which of these numbers divides exactly by 6? (a) 2734 (b) 9552 (c) 4557 (d) 6200
10. 10.Which of these numbers divides exactly by 11? (a) 1274 (b) 4429 (c) 1914 (d) 2958
11. 11.How many factors does 75 have?
12. 12.Which of these numbers divides exactly by 3? (a) 4233 (b) 6332 (c) 8551 (d) 5683
13. 13.Which of these numbers divides exactly by 11? (a) 3392 (b) 7898 (c) 5864 (d) 9685
14. 14.How many factors does 14 have?
15. 15.Which of these numbers divides exactly by 6? (a) 4382 (b) 1666 (c) 1794 (d) 5264
16. 16.What is the smallest number you must take away from 136 so that it divides exactly by 12?
17. 17.How many factors does 38 have?
18. 18.How many factors does 19 have?
19. 19.Which of these numbers divides exactly by 4? (a) 1651 (b) 3235 (c) 3260 (d) 3166
20. 20.How many factors does 87 have?
21. 21.How many factors does 32 have?
22. 22.Which of these numbers divides exactly by 3? (a) 1168 (b) 1642 (c) 5347 (d) 8238
23. 23.What is the smallest number you must add to 177 so that it divides exactly by 6?
24. 24.What is the smallest number you must take away from 853 so that it divides exactly by 7?
25. 25.Which of these numbers divides exactly by 11? (a) 6550 (b) 3109 (c) 9541 (d) 4719
26. 26.Which of these numbers divides exactly by 9? (a) 6803 (b) 5346 (c) 3004 (d) 2794
27. 27.How many factors does 93 have?
28. 28.Which of these numbers divides exactly by 6? (a) 3378 (b) 9010 (c) 1251 (d) 3721
29. 29.What is the smallest number you must add to 124 so that it divides exactly by 7?
30. 30.What is the smallest number you must take away from 409 so that it divides exactly by 8?
31. 31.What is the smallest number you must add to 467 so that it divides exactly by 3?
32. 32.Which of these numbers divides exactly by 11? (a) 2495 (b) 1606 (c) 1923 (d) 8625
33. 33.What is the smallest number you must add to 741 so that it divides exactly by 11?
34. 34.Which of these numbers divides exactly by 4? (a) 6710 (b) 2835 (c) 1752 (d) 1903
35. 35.Which of these numbers divides exactly by 8? (a) 2427 (b) 4251 (c) 9222 (d) 6128
36. 36.Which of these numbers divides exactly by 4? (a) 5136 (b) 2067 (c) 6973 (d) 5959
37. 37.What is the smallest number you must add to 567 so that it divides exactly by 8?
38. 38.Which of these numbers divides exactly by 6? (a) 9979 (b) 8933 (c) 6453 (d) 1014
39. 39.What is the smallest number you must add to 605 so that it divides exactly by 8?
40. 40.How many factors does 16 have?

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