Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 161 · 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 46 have?
2. 2.How many factors does 73 have?
3. 3.Which of these numbers divides exactly by 4? (a) 8852 (b) 2949 (c) 2893 (d) 7611
4. 4.What is the smallest number you must add to 608 so that it divides exactly by 12?
5. 5.What is the smallest number you must take away from 446 so that it divides exactly by 7?
6. 6.How many factors does 37 have?
7. 7.What is the smallest number you must add to 910 so that it divides exactly by 8?
8. 8.How many factors does 84 have?
9. 9.Which of these numbers divides exactly by 9? (a) 6139 (b) 9229 (c) 2369 (d) 6840
10. 10.What is the smallest number you must add to 374 so that it divides exactly by 6?
11. 11.Which of these numbers divides exactly by 9? (a) 3611 (b) 4311 (c) 6636 (d) 4810
12. 12.What is the smallest number you must add to 286 so that it divides exactly by 3?
13. 13.What is the smallest number you must add to 986 so that it divides exactly by 13?
14. 14.What is the smallest number you must add to 386 so that it divides exactly by 7?
15. 15.Which of these numbers divides exactly by 4? (a) 2253 (b) 1392 (c) 1013 (d) 5315
16. 16.What is the smallest number you must take away from 254 so that it divides exactly by 11?
17. 17.What is the smallest number you must take away from 566 so that it divides exactly by 8?
18. 18.What is the smallest number you must take away from 917 so that it divides exactly by 13?
19. 19.How many factors does 33 have?
20. 20.Which of these numbers divides exactly by 9? (a) 7445 (b) 7113 (c) 2236 (d) 3393
21. 21.How many factors does 83 have?
22. 22.What is the smallest number you must add to 944 so that it divides exactly by 13?
23. 23.How many factors does 19 have?
24. 24.What is the smallest number you must take away from 122 so that it divides exactly by 6?
25. 25.Which of these numbers divides exactly by 9? (a) 6680 (b) 1340 (c) 9542 (d) 6021
26. 26.Which of these numbers divides exactly by 3? (a) 9940 (b) 8616 (c) 5165 (d) 9749
27. 27.How many factors does 59 have?
28. 28.How many factors does 16 have?
29. 29.Which of these numbers divides exactly by 11? (a) 1657 (b) 7877 (c) 3730 (d) 9262
30. 30.What is the smallest number you must add to 571 so that it divides exactly by 6?
31. 31.What is the smallest number you must take away from 662 so that it divides exactly by 12?
32. 32.How many factors does 100 have?
33. 33.What is the smallest number you must take away from 987 so that it divides exactly by 11?
34. 34.What is the smallest number you must add to 839 so that it divides exactly by 7?
35. 35.What is the smallest number you must add to 611 so that it divides exactly by 8?
36. 36.What is the smallest number you must add to 661 so that it divides exactly by 11?
37. 37.Which of these numbers divides exactly by 4? (a) 6651 (b) 4307 (c) 6402 (d) 5652
38. 38.What is the smallest number you must add to 183 so that it divides exactly by 4?
39. 39.How many factors does 67 have?
40. 40.What is the smallest number you must take away from 276 so that it divides exactly by 9?

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