Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 68 · 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 take away from 629 so that it divides exactly by 6?
2. 2.How many factors does 96 have?
3. 3.What is the smallest number you must take away from 107 so that it divides exactly by 12?
4. 4.How many factors does 21 have?
5. 5.Which of these numbers divides exactly by 4? (a) 4171 (b) 6933 (c) 9573 (d) 3224
6. 6.What is the smallest number you must take away from 801 so that it divides exactly by 7?
7. 7.How many factors does 90 have?
8. 8.What is the smallest number you must take away from 445 so that it divides exactly by 6?
9. 9.What is the smallest number you must take away from 355 so that it divides exactly by 9?
10. 10.Which of these numbers divides exactly by 8? (a) 5641 (b) 2144 (c) 6326 (d) 1657
11. 11.What is the smallest number you must add to 414 so that it divides exactly by 8?
12. 12.Which of these numbers divides exactly by 6? (a) 2950 (b) 1694 (c) 4040 (d) 1026
13. 13.How many factors does 31 have?
14. 14.How many factors does 53 have?
15. 15.What is the smallest number you must take away from 758 so that it divides exactly by 12?
16. 16.How many factors does 93 have?
17. 17.What is the smallest number you must take away from 273 so that it divides exactly by 4?
18. 18.What is the smallest number you must add to 523 so that it divides exactly by 3?
19. 19.What is the smallest number you must take away from 764 so that it divides exactly by 8?
20. 20.How many factors does 16 have?
21. 21.Which of these numbers divides exactly by 11? (a) 2112 (b) 8320 (c) 2501 (d) 1311
22. 22.What is the smallest number you must take away from 175 so that it divides exactly by 6?
23. 23.How many factors does 46 have?
24. 24.What is the smallest number you must add to 492 so that it divides exactly by 11?
25. 25.What is the smallest number you must take away from 363 so that it divides exactly by 4?
26. 26.Which of these numbers divides exactly by 6? (a) 5788 (b) 2825 (c) 6798 (d) 8351
27. 27.What is the smallest number you must take away from 744 so that it divides exactly by 7?
28. 28.What is the smallest number you must add to 243 so that it divides exactly by 7?
29. 29.What is the smallest number you must add to 662 so that it divides exactly by 4?
30. 30.How many factors does 66 have?
31. 31.Which of these numbers divides exactly by 4? (a) 7694 (b) 1417 (c) 3104 (d) 3441
32. 32.Which of these numbers divides exactly by 6? (a) 5052 (b) 3231 (c) 8909 (d) 5311
33. 33.Which of these numbers divides exactly by 4? (a) 5066 (b) 3081 (c) 9128 (d) 8734
34. 34.What is the smallest number you must take away from 949 so that it divides exactly by 9?
35. 35.What is the smallest number you must add to 371 so that it divides exactly by 12?
36. 36.What is the smallest number you must take away from 793 so that it divides exactly by 7?
37. 37.What is the smallest number you must add to 319 so that it divides exactly by 9?
38. 38.Which of these numbers divides exactly by 8? (a) 6268 (b) 2044 (c) 4329 (d) 1968
39. 39.How many factors does 86 have?
40. 40.What is the smallest number you must add to 481 so that it divides exactly by 3?

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