Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 93 · 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 695 so that it divides exactly by 6?
2. 2.How many factors does 99 have?
3. 3.Which of these numbers divides exactly by 9? (a) 8745 (b) 3608 (c) 2562 (d) 1350
4. 4.How many factors does 79 have?
5. 5.Which of these numbers divides exactly by 4? (a) 3032 (b) 9823 (c) 1609 (d) 3183
6. 6.What is the smallest number you must add to 367 so that it divides exactly by 12?
7. 7.What is the smallest number you must take away from 987 so that it divides exactly by 4?
8. 8.How many factors does 18 have?
9. 9.What is the smallest number you must take away from 771 so that it divides exactly by 9?
10. 10.Which of these numbers divides exactly by 3? (a) 3383 (b) 9507 (c) 7183 (d) 3380
11. 11.How many factors does 80 have?
12. 12.How many factors does 32 have?
13. 13.How many factors does 31 have?
14. 14.What is the smallest number you must take away from 106 so that it divides exactly by 12?
15. 15.How many factors does 65 have?
16. 16.What is the smallest number you must add to 953 so that it divides exactly by 13?
17. 17.Which of these numbers divides exactly by 3? (a) 9829 (b) 3707 (c) 1594 (d) 2694
18. 18.What is the smallest number you must take away from 584 so that it divides exactly by 7?
19. 19.Which of these numbers divides exactly by 4? (a) 8561 (b) 1108 (c) 7402 (d) 2527
20. 20.What is the smallest number you must take away from 545 so that it divides exactly by 9?
21. 21.How many factors does 52 have?
22. 22.What is the smallest number you must take away from 822 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 760 so that it divides exactly by 13?
24. 24.How many factors does 54 have?
25. 25.How many factors does 85 have?
26. 26.Which of these numbers divides exactly by 6? (a) 6354 (b) 9952 (c) 9429 (d) 1715
27. 27.What is the smallest number you must add to 629 so that it divides exactly by 12?
28. 28.Which of these numbers divides exactly by 11? (a) 7656 (b) 7248 (c) 3139 (d) 6683
29. 29.What is the smallest number you must take away from 632 so that it divides exactly by 11?
30. 30.What is the smallest number you must take away from 773 so that it divides exactly by 9?
31. 31.Which of these numbers divides exactly by 6? (a) 8342 (b) 2508 (c) 1697 (d) 8672
32. 32.Which of these numbers divides exactly by 11? (a) 4438 (b) 1611 (c) 3017 (d) 2926
33. 33.What is the smallest number you must take away from 869 so that it divides exactly by 6?
34. 34.Which of these numbers divides exactly by 3? (a) 8442 (b) 8497 (c) 6406 (d) 4964
35. 35.What is the smallest number you must add to 698 so that it divides exactly by 3?
36. 36.What is the smallest number you must add to 275 so that it divides exactly by 13?
37. 37.What is the smallest number you must take away from 428 so that it divides exactly by 11?
38. 38.How many factors does 39 have?
39. 39.Which of these numbers divides exactly by 11? (a) 4114 (b) 2074 (c) 7522 (d) 1880
40. 40.Which of these numbers divides exactly by 9? (a) 6453 (b) 7720 (c) 6059 (d) 5182

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