Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 69 · 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 27 have?
2. 2.Which of these numbers divides exactly by 4? (a) 8359 (b) 4421 (c) 9072 (d) 2079
3. 3.What is the smallest number you must add to 809 so that it divides exactly by 8?
4. 4.How many factors does 30 have?
5. 5.Which of these numbers divides exactly by 9? (a) 8893 (b) 2098 (c) 5601 (d) 3888
6. 6.What is the smallest number you must add to 650 so that it divides exactly by 7?
7. 7.How many factors does 50 have?
8. 8.How many factors does 37 have?
9. 9.How many factors does 43 have?
10. 10.Which of these numbers divides exactly by 4? (a) 4030 (b) 7224 (c) 2694 (d) 5373
11. 11.What is the smallest number you must take away from 770 so that it divides exactly by 4?
12. 12.Which of these numbers divides exactly by 3? (a) 8311 (b) 3198 (c) 1795 (d) 9754
13. 13.What is the smallest number you must add to 228 so that it divides exactly by 13?
14. 14.What is the smallest number you must take away from 593 so that it divides exactly by 11?
15. 15.How many factors does 19 have?
16. 16.What is the smallest number you must add to 153 so that it divides exactly by 8?
17. 17.How many factors does 91 have?
18. 18.Which of these numbers divides exactly by 11? (a) 5559 (b) 9807 (c) 4070 (d) 1330
19. 19.What is the smallest number you must add to 304 so that it divides exactly by 7?
20. 20.How many factors does 45 have?
21. 21.Which of these numbers divides exactly by 8? (a) 7227 (b) 4103 (c) 2250 (d) 7960
22. 22.What is the smallest number you must take away from 944 so that it divides exactly by 7?
23. 23.What is the smallest number you must add to 552 so that it divides exactly by 9?
24. 24.How many factors does 47 have?
25. 25.How many factors does 33 have?
26. 26.Which of these numbers divides exactly by 8? (a) 8205 (b) 4257 (c) 2808 (d) 9578
27. 27.What is the smallest number you must take away from 497 so that it divides exactly by 9?
28. 28.What is the smallest number you must add to 978 so that it divides exactly by 12?
29. 29.What is the smallest number you must take away from 109 so that it divides exactly by 6?
30. 30.What is the smallest number you must add to 863 so that it divides exactly by 8?
31. 31.What is the smallest number you must take away from 970 so that it divides exactly by 9?
32. 32.What is the smallest number you must take away from 579 so that it divides exactly by 12?
33. 33.What is the smallest number you must take away from 130 so that it divides exactly by 9?
34. 34.Which of these numbers divides exactly by 6? (a) 4535 (b) 9486 (c) 8231 (d) 1541
35. 35.What is the smallest number you must take away from 358 so that it divides exactly by 4?
36. 36.How many factors does 49 have?
37. 37.How many factors does 41 have?
38. 38.What is the smallest number you must add to 478 so that it divides exactly by 9?
39. 39.What is the smallest number you must add to 369 so that it divides exactly by 6?
40. 40.What is the smallest number you must add to 613 so that it divides exactly by 7?

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