Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 119 · 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 167 so that it divides exactly by 6?
2. 2.Which of these numbers divides exactly by 3? (a) 6353 (b) 9947 (c) 2308 (d) 4959
3. 3.What is the smallest number you must add to 790 so that it divides exactly by 11?
4. 4.Which of these numbers divides exactly by 4? (a) 6871 (b) 1941 (c) 1907 (d) 1012
5. 5.Which of these numbers divides exactly by 3? (a) 8929 (b) 9636 (c) 3013 (d) 8051
6. 6.What is the smallest number you must take away from 548 so that it divides exactly by 7?
7. 7.What is the smallest number you must take away from 865 so that it divides exactly by 3?
8. 8.Which of these numbers divides exactly by 3? (a) 5018 (b) 5861 (c) 6830 (d) 5925
9. 9.What is the smallest number you must take away from 938 so that it divides exactly by 8?
10. 10.What is the smallest number you must add to 555 so that it divides exactly by 13?
11. 11.Which of these numbers divides exactly by 3? (a) 3429 (b) 2324 (c) 1456 (d) 7573
12. 12.Which of these numbers divides exactly by 8? (a) 8112 (b) 5732 (c) 2225 (d) 8711
13. 13.Which of these numbers divides exactly by 11? (a) 2864 (b) 1728 (c) 3791 (d) 1232
14. 14.Which of these numbers divides exactly by 8? (a) 6470 (b) 9312 (c) 9495 (d) 6283
15. 15.What is the smallest number you must take away from 370 so that it divides exactly by 7?
16. 16.What is the smallest number you must take away from 579 so that it divides exactly by 7?
17. 17.How many factors does 79 have?
18. 18.What is the smallest number you must take away from 155 so that it divides exactly by 12?
19. 19.What is the smallest number you must add to 294 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 632 so that it divides exactly by 9?
21. 21.What is the smallest number you must add to 284 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 212 so that it divides exactly by 12?
23. 23.What is the smallest number you must add to 118 so that it divides exactly by 4?
24. 24.How many factors does 33 have?
25. 25.How many factors does 37 have?
26. 26.What is the smallest number you must take away from 570 so that it divides exactly by 11?
27. 27.How many factors does 89 have?
28. 28.Which of these numbers divides exactly by 8? (a) 3522 (b) 7498 (c) 5371 (d) 4624
29. 29.What is the smallest number you must take away from 282 so that it divides exactly by 12?
30. 30.How many factors does 12 have?
31. 31.What is the smallest number you must add to 378 so that it divides exactly by 4?
32. 32.What is the smallest number you must take away from 247 so that it divides exactly by 6?
33. 33.How many factors does 29 have?
34. 34.What is the smallest number you must take away from 239 so that it divides exactly by 13?
35. 35.Which of these numbers divides exactly by 8? (a) 1524 (b) 2332 (c) 7280 (d) 1865
36. 36.How many factors does 31 have?
37. 37.How many factors does 32 have?
38. 38.What is the smallest number you must take away from 199 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 6? (a) 6632 (b) 4718 (c) 6832 (d) 9630
40. 40.How many factors does 94 have?

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