Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 191 · 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.Which of these numbers divides exactly by 11? (a) 1700 (b) 3147 (c) 5936 (d) 7975
2. 2.What is the smallest number you must add to 138 so that it divides exactly by 4?
3. 3.What is the smallest number you must add to 250 so that it divides exactly by 4?
4. 4.How many factors does 58 have?
5. 5.What is the smallest number you must add to 432 so that it divides exactly by 13?
6. 6.What is the smallest number you must add to 143 so that it divides exactly by 6?
7. 7.What is the smallest number you must take away from 959 so that it divides exactly by 11?
8. 8.What is the smallest number you must add to 477 so that it divides exactly by 4?
9. 9.What is the smallest number you must add to 781 so that it divides exactly by 8?
10. 10.Which of these numbers divides exactly by 3? (a) 5628 (b) 2306 (c) 5662 (d) 9383
11. 11.What is the smallest number you must take away from 841 so that it divides exactly by 7?
12. 12.How many factors does 48 have?
13. 13.Which of these numbers divides exactly by 11? (a) 1886 (b) 5091 (c) 2515 (d) 4257
14. 14.What is the smallest number you must add to 669 so that it divides exactly by 13?
15. 15.What is the smallest number you must add to 430 so that it divides exactly by 9?
16. 16.What is the smallest number you must take away from 373 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 932 so that it divides exactly by 8?
18. 18.Which of these numbers divides exactly by 3? (a) 2086 (b) 5253 (c) 9286 (d) 2017
19. 19.Which of these numbers divides exactly by 9? (a) 8840 (b) 6531 (c) 1638 (d) 5183
20. 20.Which of these numbers divides exactly by 9? (a) 9836 (b) 5467 (c) 5058 (d) 1613
21. 21.What is the smallest number you must add to 522 so that it divides exactly by 11?
22. 22.Which of these numbers divides exactly by 3? (a) 8915 (b) 1861 (c) 6021 (d) 2756
23. 23.Which of these numbers divides exactly by 6? (a) 2722 (b) 5975 (c) 8489 (d) 4602
24. 24.What is the smallest number you must add to 681 so that it divides exactly by 4?
25. 25.How many factors does 67 have?
26. 26.Which of these numbers divides exactly by 11? (a) 4208 (b) 1177 (c) 5948 (d) 4716
27. 27.What is the smallest number you must add to 388 so that it divides exactly by 7?
28. 28.What is the smallest number you must add to 486 so that it divides exactly by 4?
29. 29.How many factors does 33 have?
30. 30.What is the smallest number you must take away from 202 so that it divides exactly by 4?
31. 31.What is the smallest number you must take away from 964 so that it divides exactly by 6?
32. 32.What is the smallest number you must add to 446 so that it divides exactly by 6?
33. 33.What is the smallest number you must add to 434 so that it divides exactly by 9?
34. 34.What is the smallest number you must take away from 283 so that it divides exactly by 3?
35. 35.How many factors does 40 have?
36. 36.What is the smallest number you must add to 282 so that it divides exactly by 8?
37. 37.What is the smallest number you must add to 414 so that it divides exactly by 4?
38. 38.What is the smallest number you must add to 115 so that it divides exactly by 11?
39. 39.How many factors does 62 have?
40. 40.How many factors does 54 have?

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