Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 73 · 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 436 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 655 so that it divides exactly by 4?
3. 3.How many factors does 61 have?
4. 4.Which of these numbers divides exactly by 3? (a) 5644 (b) 7495 (c) 9945 (d) 8563
5. 5.How many factors does 63 have?
6. 6.What is the smallest number you must take away from 179 so that it divides exactly by 11?
7. 7.What is the smallest number you must take away from 526 so that it divides exactly by 4?
8. 8.What is the smallest number you must take away from 355 so that it divides exactly by 11?
9. 9.Which of these numbers divides exactly by 4? (a) 8233 (b) 4936 (c) 2489 (d) 7131
10. 10.What is the smallest number you must add to 173 so that it divides exactly by 11?
11. 11.How many factors does 92 have?
12. 12.What is the smallest number you must take away from 685 so that it divides exactly by 6?
13. 13.How many factors does 65 have?
14. 14.How many factors does 29 have?
15. 15.Which of these numbers divides exactly by 8? (a) 3064 (b) 5979 (c) 4804 (d) 8959
16. 16.How many factors does 28 have?
17. 17.Which of these numbers divides exactly by 8? (a) 2681 (b) 6147 (c) 1192 (d) 1613
18. 18.What is the smallest number you must take away from 475 so that it divides exactly by 6?
19. 19.What is the smallest number you must add to 804 so that it divides exactly by 9?
20. 20.How many factors does 32 have?
21. 21.Which of these numbers divides exactly by 4? (a) 8945 (b) 2907 (c) 5129 (d) 7712
22. 22.Which of these numbers divides exactly by 3? (a) 9671 (b) 7185 (c) 5788 (d) 6515
23. 23.How many factors does 45 have?
24. 24.What is the smallest number you must take away from 999 so that it divides exactly by 7?
25. 25.What is the smallest number you must add to 990 so that it divides exactly by 13?
26. 26.How many factors does 94 have?
27. 27.What is the smallest number you must add to 316 so that it divides exactly by 9?
28. 28.Which of these numbers divides exactly by 4? (a) 2858 (b) 8006 (c) 4883 (d) 8892
29. 29.Which of these numbers divides exactly by 9? (a) 8644 (b) 6958 (c) 8749 (d) 9936
30. 30.Which of these numbers divides exactly by 4? (a) 8677 (b) 3181 (c) 2022 (d) 4192
31. 31.What is the smallest number you must take away from 804 so that it divides exactly by 7?
32. 32.How many factors does 74 have?
33. 33.Which of these numbers divides exactly by 4? (a) 3475 (b) 9091 (c) 2765 (d) 4904
34. 34.How many factors does 23 have?
35. 35.Which of these numbers divides exactly by 8? (a) 3274 (b) 1200 (c) 9986 (d) 3668
36. 36.What is the smallest number you must take away from 557 so that it divides exactly by 6?
37. 37.Which of these numbers divides exactly by 3? (a) 1967 (b) 2773 (c) 9000 (d) 4877
38. 38.Which of these numbers divides exactly by 6? (a) 5651 (b) 5323 (c) 6670 (d) 5322
39. 39.What is the smallest number you must add to 226 so that it divides exactly by 11?
40. 40.How many factors does 90 have?

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