Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 45 · 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 350 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 985 so that it divides exactly by 13?
3. 3.What is the smallest number you must take away from 510 so that it divides exactly by 7?
4. 4.What is the smallest number you must take away from 260 so that it divides exactly by 3?
5. 5.How many factors does 25 have?
6. 6.What is the smallest number you must add to 785 so that it divides exactly by 6?
7. 7.How many factors does 75 have?
8. 8.What is the smallest number you must take away from 236 so that it divides exactly by 9?
9. 9.How many factors does 45 have?
10. 10.How many factors does 61 have?
11. 11.What is the smallest number you must take away from 608 so that it divides exactly by 13?
12. 12.Which of these numbers divides exactly by 6? (a) 5486 (b) 7178 (c) 1208 (d) 4656
13. 13.How many factors does 57 have?
14. 14.How many factors does 36 have?
15. 15.How many factors does 69 have?
16. 16.What is the smallest number you must take away from 634 so that it divides exactly by 4?
17. 17.What is the smallest number you must add to 334 so that it divides exactly by 8?
18. 18.Which of these numbers divides exactly by 4? (a) 5153 (b) 5168 (c) 4326 (d) 9402
19. 19.Which of these numbers divides exactly by 6? (a) 7963 (b) 7025 (c) 4452 (d) 3161
20. 20.How many factors does 63 have?
21. 21.Which of these numbers divides exactly by 9? (a) 1817 (b) 5625 (c) 5434 (d) 2354
22. 22.Which of these numbers divides exactly by 11? (a) 9467 (b) 4778 (c) 4847 (d) 9449
23. 23.Which of these numbers divides exactly by 3? (a) 1516 (b) 6776 (c) 4549 (d) 1902
24. 24.What is the smallest number you must take away from 701 so that it divides exactly by 12?
25. 25.How many factors does 48 have?
26. 26.What is the smallest number you must add to 530 so that it divides exactly by 3?
27. 27.What is the smallest number you must take away from 461 so that it divides exactly by 4?
28. 28.What is the smallest number you must take away from 196 so that it divides exactly by 8?
29. 29.Which of these numbers divides exactly by 11? (a) 4408 (b) 3436 (c) 1353 (d) 7940
30. 30.Which of these numbers divides exactly by 4? (a) 9659 (b) 2652 (c) 6007 (d) 3219
31. 31.Which of these numbers divides exactly by 8? (a) 1616 (b) 9323 (c) 1852 (d) 3461
32. 32.What is the smallest number you must take away from 309 so that it divides exactly by 7?
33. 33.What is the smallest number you must add to 151 so that it divides exactly by 13?
34. 34.What is the smallest number you must take away from 681 so that it divides exactly by 7?
35. 35.Which of these numbers divides exactly by 8? (a) 3810 (b) 3168 (c) 1185 (d) 7974
36. 36.What is the smallest number you must take away from 434 so that it divides exactly by 13?
37. 37.How many factors does 14 have?
38. 38.Which of these numbers divides exactly by 3? (a) 5149 (b) 9070 (c) 8360 (d) 5160
39. 39.What is the smallest number you must take away from 655 so that it divides exactly by 11?
40. 40.What is the smallest number you must take away from 761 so that it divides exactly by 11?

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