Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 139 · 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 61 have?
2. 2.How many factors does 41 have?
3. 3.What is the smallest number you must take away from 611 so that it divides exactly by 11?
4. 4.Which of these numbers divides exactly by 6? (a) 2339 (b) 6662 (c) 8967 (d) 3432
5. 5.What is the smallest number you must take away from 622 so that it divides exactly by 9?
6. 6.What is the smallest number you must take away from 979 so that it divides exactly by 4?
7. 7.Which of these numbers divides exactly by 9? (a) 9572 (b) 5494 (c) 8298 (d) 2896
8. 8.How many factors does 16 have?
9. 9.What is the smallest number you must add to 492 so that it divides exactly by 11?
10. 10.What is the smallest number you must take away from 289 so that it divides exactly by 12?
11. 11.What is the smallest number you must add to 223 so that it divides exactly by 7?
12. 12.What is the smallest number you must add to 630 so that it divides exactly by 8?
13. 13.What is the smallest number you must add to 479 so that it divides exactly by 6?
14. 14.How many factors does 67 have?
15. 15.What is the smallest number you must take away from 137 so that it divides exactly by 6?
16. 16.How many factors does 38 have?
17. 17.Which of these numbers divides exactly by 8? (a) 6861 (b) 8048 (c) 7551 (d) 6679
18. 18.What is the smallest number you must take away from 622 so that it divides exactly by 4?
19. 19.What is the smallest number you must take away from 661 so that it divides exactly by 7?
20. 20.What is the smallest number you must take away from 315 so that it divides exactly by 4?
21. 21.How many factors does 34 have?
22. 22.Which of these numbers divides exactly by 11? (a) 1628 (b) 7930 (c) 7686 (d) 5716
23. 23.Which of these numbers divides exactly by 3? (a) 8257 (b) 9134 (c) 3358 (d) 7011
24. 24.How many factors does 33 have?
25. 25.Which of these numbers divides exactly by 3? (a) 5515 (b) 6927 (c) 4478 (d) 4681
26. 26.What is the smallest number you must add to 740 so that it divides exactly by 8?
27. 27.Which of these numbers divides exactly by 4? (a) 2693 (b) 7343 (c) 5952 (d) 8695
28. 28.What is the smallest number you must take away from 814 so that it divides exactly by 6?
29. 29.How many factors does 48 have?
30. 30.How many factors does 52 have?
31. 31.What is the smallest number you must add to 529 so that it divides exactly by 7?
32. 32.What is the smallest number you must take away from 987 so that it divides exactly by 12?
33. 33.How many factors does 79 have?
34. 34.What is the smallest number you must add to 823 so that it divides exactly by 6?
35. 35.How many factors does 27 have?
36. 36.How many factors does 37 have?
37. 37.Which of these numbers divides exactly by 3? (a) 6913 (b) 4505 (c) 1398 (d) 1747
38. 38.What is the smallest number you must add to 556 so that it divides exactly by 8?
39. 39.Which of these numbers divides exactly by 9? (a) 6121 (b) 7137 (c) 3980 (d) 8229
40. 40.Which of these numbers divides exactly by 6? (a) 5510 (b) 6676 (c) 6766 (d) 2046

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