Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 134 · 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 add to 215 so that it divides exactly by 7?
2. 2.Which of these numbers divides exactly by 4? (a) 9583 (b) 9446 (c) 1387 (d) 7668
3. 3.What is the smallest number you must add to 370 so that it divides exactly by 13?
4. 4.Which of these numbers divides exactly by 11? (a) 3641 (b) 3482 (c) 6650 (d) 4764
5. 5.What is the smallest number you must add to 185 so that it divides exactly by 11?
6. 6.How many factors does 89 have?
7. 7.What is the smallest number you must take away from 452 so that it divides exactly by 11?
8. 8.How many factors does 88 have?
9. 9.What is the smallest number you must take away from 149 so that it divides exactly by 3?
10. 10.How many factors does 26 have?
11. 11.Which of these numbers divides exactly by 3? (a) 9644 (b) 6166 (c) 7834 (d) 7017
12. 12.Which of these numbers divides exactly by 4? (a) 1337 (b) 2463 (c) 8431 (d) 3972
13. 13.What is the smallest number you must take away from 145 so that it divides exactly by 8?
14. 14.Which of these numbers divides exactly by 8? (a) 5353 (b) 4829 (c) 6280 (d) 6925
15. 15.Which of these numbers divides exactly by 3? (a) 9665 (b) 4532 (c) 7104 (d) 3545
16. 16.Which of these numbers divides exactly by 11? (a) 6241 (b) 3703 (c) 2580 (d) 1210
17. 17.What is the smallest number you must add to 176 so that it divides exactly by 9?
18. 18.Which of these numbers divides exactly by 4? (a) 2158 (b) 1892 (c) 1173 (d) 4953
19. 19.What is the smallest number you must take away from 564 so that it divides exactly by 13?
20. 20.What is the smallest number you must add to 326 so that it divides exactly by 6?
21. 21.What is the smallest number you must add to 263 so that it divides exactly by 7?
22. 22.How many factors does 47 have?
23. 23.How many factors does 46 have?
24. 24.How many factors does 87 have?
25. 25.What is the smallest number you must take away from 303 so that it divides exactly by 9?
26. 26.How many factors does 70 have?
27. 27.How many factors does 80 have?
28. 28.What is the smallest number you must add to 620 so that it divides exactly by 12?
29. 29.Which of these numbers divides exactly by 8? (a) 2407 (b) 7952 (c) 1705 (d) 1487
30. 30.What is the smallest number you must add to 777 so that it divides exactly by 4?
31. 31.How many factors does 75 have?
32. 32.How many factors does 77 have?
33. 33.Which of these numbers divides exactly by 8? (a) 5404 (b) 9105 (c) 3472 (d) 3427
34. 34.What is the smallest number you must add to 518 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 766 so that it divides exactly by 7?
36. 36.What is the smallest number you must add to 699 so that it divides exactly by 7?
37. 37.What is the smallest number you must take away from 187 so that it divides exactly by 8?
38. 38.Which of these numbers divides exactly by 4? (a) 3738 (b) 2738 (c) 7523 (d) 6332
39. 39.How many factors does 22 have?
40. 40.How many factors does 98 have?

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