Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 272 · 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 add to 830 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 539 so that it divides exactly by 8?
3. 3.Which of these numbers divides exactly by 11? (a) 3004 (b) 6979 (c) 7639 (d) 8998
4. 4.What is the smallest number you must add to 142 so that it divides exactly by 9?
5. 5.How many factors does 57 have?
6. 6.What is the smallest number you must add to 410 so that it divides exactly by 9?
7. 7.What is the smallest number you must take away from 947 so that it divides exactly by 12?
8. 8.What is the smallest number you must add to 843 so that it divides exactly by 12?
9. 9.How many factors does 53 have?
10. 10.Which of these numbers divides exactly by 4? (a) 5357 (b) 5508 (c) 1066 (d) 7891
11. 11.What is the smallest number you must add to 647 so that it divides exactly by 3?
12. 12.How many factors does 20 have?
13. 13.Which of these numbers divides exactly by 6? (a) 1424 (b) 2273 (c) 2550 (d) 4198
14. 14.What is the smallest number you must add to 734 so that it divides exactly by 3?
15. 15.What is the smallest number you must add to 280 so that it divides exactly by 11?
16. 16.What is the smallest number you must take away from 831 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 8? (a) 9505 (b) 6289 (c) 4365 (d) 1784
18. 18.Which of these numbers divides exactly by 6? (a) 1662 (b) 8498 (c) 8708 (d) 9681
19. 19.Which of these numbers divides exactly by 8? (a) 5996 (b) 2765 (c) 4752 (d) 1014
20. 20.What is the smallest number you must take away from 301 so that it divides exactly by 4?
21. 21.How many factors does 24 have?
22. 22.What is the smallest number you must add to 466 so that it divides exactly by 13?
23. 23.How many factors does 31 have?
24. 24.What is the smallest number you must take away from 895 so that it divides exactly by 11?
25. 25.Which of these numbers divides exactly by 3? (a) 4049 (b) 5256 (c) 2956 (d) 4072
26. 26.What is the smallest number you must add to 128 so that it divides exactly by 6?
27. 27.Which of these numbers divides exactly by 4? (a) 6013 (b) 4192 (c) 7279 (d) 1106
28. 28.Which of these numbers divides exactly by 8? (a) 9546 (b) 6198 (c) 4179 (d) 9056
29. 29.Which of these numbers divides exactly by 3? (a) 4480 (b) 6856 (c) 1598 (d) 5961
30. 30.How many factors does 85 have?
31. 31.What is the smallest number you must add to 890 so that it divides exactly by 7?
32. 32.How many factors does 96 have?
33. 33.How many factors does 43 have?
34. 34.How many factors does 97 have?
35. 35.Which of these numbers divides exactly by 8? (a) 8735 (b) 3512 (c) 8108 (d) 7029
36. 36.What is the smallest number you must add to 307 so that it divides exactly by 9?
37. 37.How many factors does 89 have?
38. 38.Which of these numbers divides exactly by 11? (a) 7752 (b) 6534 (c) 4205 (d) 6384
39. 39.What is the smallest number you must take away from 577 so that it divides exactly by 3?
40. 40.Which of these numbers divides exactly by 6? (a) 6599 (b) 2709 (c) 6537 (d) 8784

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