Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 145 · 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 4? (a) 3519 (b) 5336 (c) 5798 (d) 3378
2. 2.Which of these numbers divides exactly by 9? (a) 6425 (b) 9521 (c) 6832 (d) 5517
3. 3.How many factors does 89 have?
4. 4.Which of these numbers divides exactly by 6? (a) 2193 (b) 1552 (c) 2712 (d) 9107
5. 5.How many factors does 20 have?
6. 6.What is the smallest number you must add to 497 so that it divides exactly by 4?
7. 7.Which of these numbers divides exactly by 3? (a) 8321 (b) 8029 (c) 1207 (d) 5517
8. 8.How many factors does 45 have?
9. 9.What is the smallest number you must take away from 334 so that it divides exactly by 4?
10. 10.Which of these numbers divides exactly by 3? (a) 8464 (b) 2293 (c) 3120 (d) 9137
11. 11.Which of these numbers divides exactly by 8? (a) 7284 (b) 3136 (c) 6326 (d) 3899
12. 12.What is the smallest number you must take away from 473 so that it divides exactly by 8?
13. 13.What is the smallest number you must take away from 790 so that it divides exactly by 11?
14. 14.Which of these numbers divides exactly by 11? (a) 1976 (b) 3467 (c) 2376 (d) 3572
15. 15.What is the smallest number you must add to 951 so that it divides exactly by 12?
16. 16.How many factors does 37 have?
17. 17.How many factors does 90 have?
18. 18.How many factors does 82 have?
19. 19.Which of these numbers divides exactly by 3? (a) 2670 (b) 1100 (c) 1828 (d) 6436
20. 20.How many factors does 100 have?
21. 21.What is the smallest number you must take away from 304 so that it divides exactly by 6?
22. 22.Which of these numbers divides exactly by 8? (a) 9488 (b) 1547 (c) 2548 (d) 1254
23. 23.What is the smallest number you must take away from 156 so that it divides exactly by 9?
24. 24.What is the smallest number you must take away from 231 so that it divides exactly by 9?
25. 25.How many factors does 47 have?
26. 26.How many factors does 76 have?
27. 27.What is the smallest number you must add to 407 so that it divides exactly by 6?
28. 28.How many factors does 31 have?
29. 29.How many factors does 17 have?
30. 30.Which of these numbers divides exactly by 8? (a) 6606 (b) 1016 (c) 6481 (d) 1321
31. 31.Which of these numbers divides exactly by 3? (a) 4175 (b) 4702 (c) 6802 (d) 4806
32. 32.What is the smallest number you must add to 345 so that it divides exactly by 8?
33. 33.What is the smallest number you must take away from 964 so that it divides exactly by 13?
34. 34.Which of these numbers divides exactly by 9? (a) 6586 (b) 9428 (c) 9801 (d) 6173
35. 35.What is the smallest number you must add to 869 so that it divides exactly by 7?
36. 36.Which of these numbers divides exactly by 4? (a) 8100 (b) 4511 (c) 9177 (d) 4798
37. 37.Which of these numbers divides exactly by 8? (a) 4964 (b) 1090 (c) 1232 (d) 2859
38. 38.What is the smallest number you must take away from 163 so that it divides exactly by 7?
39. 39.What is the smallest number you must add to 358 so that it divides exactly by 3?
40. 40.What is the smallest number you must take away from 639 so that it divides exactly by 4?

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