Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 216 · 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) 7541 (b) 5467 (c) 8637 (d) 9508
2. 2.How many factors does 96 have?
3. 3.How many factors does 15 have?
4. 4.What is the smallest number you must add to 800 so that it divides exactly by 6?
5. 5.What is the smallest number you must take away from 199 so that it divides exactly by 8?
6. 6.What is the smallest number you must add to 781 so that it divides exactly by 13?
7. 7.What is the smallest number you must take away from 464 so that it divides exactly by 7?
8. 8.How many factors does 18 have?
9. 9.How many factors does 41 have?
10. 10.Which of these numbers divides exactly by 4? (a) 1512 (b) 5565 (c) 7234 (d) 1910
11. 11.Which of these numbers divides exactly by 9? (a) 2538 (b) 9764 (c) 1567 (d) 9831
12. 12.How many factors does 86 have?
13. 13.How many factors does 88 have?
14. 14.How many factors does 43 have?
15. 15.Which of these numbers divides exactly by 6? (a) 2683 (b) 5745 (c) 7552 (d) 7746
16. 16.What is the smallest number you must take away from 153 so that it divides exactly by 4?
17. 17.How many factors does 85 have?
18. 18.How many factors does 21 have?
19. 19.What is the smallest number you must add to 337 so that it divides exactly by 9?
20. 20.Which of these numbers divides exactly by 6? (a) 6032 (b) 7949 (c) 4776 (d) 2549
21. 21.Which of these numbers divides exactly by 8? (a) 4522 (b) 3954 (c) 6598 (d) 7880
22. 22.What is the smallest number you must take away from 427 so that it divides exactly by 11?
23. 23.What is the smallest number you must add to 497 so that it divides exactly by 8?
24. 24.Which of these numbers divides exactly by 8? (a) 2228 (b) 2415 (c) 9105 (d) 9072
25. 25.How many factors does 93 have?
26. 26.What is the smallest number you must take away from 943 so that it divides exactly by 4?
27. 27.Which of these numbers divides exactly by 3? (a) 2030 (b) 6055 (c) 7589 (d) 1197
28. 28.What is the smallest number you must add to 121 so that it divides exactly by 6?
29. 29.What is the smallest number you must take away from 674 so that it divides exactly by 13?
30. 30.How many factors does 69 have?
31. 31.What is the smallest number you must take away from 233 so that it divides exactly by 11?
32. 32.Which of these numbers divides exactly by 8? (a) 8781 (b) 3376 (c) 7789 (d) 5174
33. 33.What is the smallest number you must take away from 547 so that it divides exactly by 3?
34. 34.What is the smallest number you must add to 823 so that it divides exactly by 11?
35. 35.How many factors does 49 have?
36. 36.What is the smallest number you must add to 350 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 241 so that it divides exactly by 6?
38. 38.What is the smallest number you must take away from 113 so that it divides exactly by 9?
39. 39.What is the smallest number you must take away from 481 so that it divides exactly by 8?
40. 40.Which of these numbers divides exactly by 4? (a) 6615 (b) 6880 (c) 2457 (d) 2255

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