Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 294 · 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 11? (a) 3322 (b) 3071 (c) 5479 (d) 3975
2. 2.What is the smallest number you must take away from 829 so that it divides exactly by 3?
3. 3.How many factors does 97 have?
4. 4.How many factors does 27 have?
5. 5.What is the smallest number you must add to 905 so that it divides exactly by 9?
6. 6.What is the smallest number you must take away from 710 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 4? (a) 1521 (b) 3495 (c) 4425 (d) 4520
8. 8.How many factors does 22 have?
9. 9.Which of these numbers divides exactly by 3? (a) 2807 (b) 3391 (c) 5532 (d) 4349
10. 10.How many factors does 18 have?
11. 11.What is the smallest number you must add to 100 so that it divides exactly by 7?
12. 12.What is the smallest number you must add to 806 so that it divides exactly by 11?
13. 13.How many factors does 75 have?
14. 14.How many factors does 29 have?
15. 15.How many factors does 76 have?
16. 16.Which of these numbers divides exactly by 11? (a) 3666 (b) 1608 (c) 8250 (d) 8638
17. 17.Which of these numbers divides exactly by 9? (a) 1424 (b) 6085 (c) 9998 (d) 4626
18. 18.What is the smallest number you must take away from 322 so that it divides exactly by 9?
19. 19.What is the smallest number you must take away from 407 so that it divides exactly by 12?
20. 20.Which of these numbers divides exactly by 8? (a) 3505 (b) 8138 (c) 7552 (d) 3597
21. 21.Which of these numbers divides exactly by 9? (a) 8371 (b) 4113 (c) 2774 (d) 5988
22. 22.How many factors does 49 have?
23. 23.What is the smallest number you must take away from 957 so that it divides exactly by 8?
24. 24.Which of these numbers divides exactly by 3? (a) 3331 (b) 7024 (c) 8461 (d) 9459
25. 25.What is the smallest number you must take away from 771 so that it divides exactly by 11?
26. 26.What is the smallest number you must add to 647 so that it divides exactly by 8?
27. 27.What is the smallest number you must add to 933 so that it divides exactly by 12?
28. 28.What is the smallest number you must take away from 475 so that it divides exactly by 3?
29. 29.How many factors does 24 have?
30. 30.Which of these numbers divides exactly by 8? (a) 6325 (b) 2532 (c) 6336 (d) 6321
31. 31.What is the smallest number you must take away from 853 so that it divides exactly by 3?
32. 32.How many factors does 47 have?
33. 33.Which of these numbers divides exactly by 9? (a) 7306 (b) 8043 (c) 5246 (d) 2295
34. 34.What is the smallest number you must take away from 277 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 6? (a) 3287 (b) 6421 (c) 1173 (d) 6222
36. 36.What is the smallest number you must add to 342 so that it divides exactly by 4?
37. 37.Which of these numbers divides exactly by 3? (a) 3766 (b) 2078 (c) 3249 (d) 1831
38. 38.What is the smallest number you must take away from 632 so that it divides exactly by 7?
39. 39.What is the smallest number you must take away from 572 so that it divides exactly by 6?
40. 40.How many factors does 71 have?

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