Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 305 · 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 6? (a) 5695 (b) 8395 (c) 3334 (d) 7062
3. 3.How many factors does 75 have?
4. 4.What is the smallest number you must take away from 234 so that it divides exactly by 12?
5. 5.What is the smallest number you must add to 414 so that it divides exactly by 4?
6. 6.Which of these numbers divides exactly by 8? (a) 5098 (b) 3667 (c) 7059 (d) 5528
7. 7.What is the smallest number you must take away from 829 so that it divides exactly by 13?
8. 8.How many factors does 60 have?
9. 9.What is the smallest number you must add to 608 so that it divides exactly by 13?
10. 10.What is the smallest number you must add to 261 so that it divides exactly by 7?
11. 11.Which of these numbers divides exactly by 4? (a) 1448 (b) 5411 (c) 1165 (d) 3978
12. 12.What is the smallest number you must add to 555 so that it divides exactly by 13?
13. 13.What is the smallest number you must add to 581 so that it divides exactly by 4?
14. 14.What is the smallest number you must add to 322 so that it divides exactly by 9?
15. 15.What is the smallest number you must add to 659 so that it divides exactly by 3?
16. 16.Which of these numbers divides exactly by 3? (a) 7143 (b) 7874 (c) 7865 (d) 2446
17. 17.How many factors does 56 have?
18. 18.What is the smallest number you must add to 537 so that it divides exactly by 11?
19. 19.What is the smallest number you must take away from 264 so that it divides exactly by 7?
20. 20.What is the smallest number you must add to 758 so that it divides exactly by 11?
21. 21.What is the smallest number you must add to 227 so that it divides exactly by 13?
22. 22.What is the smallest number you must take away from 941 so that it divides exactly by 4?
23. 23.What is the smallest number you must add to 562 so that it divides exactly by 6?
24. 24.How many factors does 25 have?
25. 25.Which of these numbers divides exactly by 9? (a) 2755 (b) 3440 (c) 1008 (d) 6590
26. 26.Which of these numbers divides exactly by 11? (a) 6204 (b) 2393 (c) 5339 (d) 8381
27. 27.What is the smallest number you must add to 337 so that it divides exactly by 11?
28. 28.How many factors does 44 have?
29. 29.What is the smallest number you must take away from 371 so that it divides exactly by 12?
30. 30.Which of these numbers divides exactly by 9? (a) 2192 (b) 8156 (c) 7422 (d) 5076
31. 31.What is the smallest number you must take away from 115 so that it divides exactly by 11?
32. 32.What is the smallest number you must take away from 457 so that it divides exactly by 4?
33. 33.How many factors does 68 have?
34. 34.What is the smallest number you must take away from 663 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 4? (a) 9991 (b) 9428 (c) 1315 (d) 6775
36. 36.Which of these numbers divides exactly by 6? (a) 7528 (b) 9587 (c) 7824 (d) 2254
37. 37.What is the smallest number you must add to 663 so that it divides exactly by 6?
38. 38.What is the smallest number you must add to 884 so that it divides exactly by 11?
39. 39.Which of these numbers divides exactly by 9? (a) 5358 (b) 9054 (c) 4713 (d) 3190
40. 40.What is the smallest number you must add to 442 so that it divides exactly by 6?

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