Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 276 · 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 353 so that it divides exactly by 12?
2. 2.What is the smallest number you must add to 948 so that it divides exactly by 9?
3. 3.What is the smallest number you must add to 985 so that it divides exactly by 8?
4. 4.What is the smallest number you must add to 280 so that it divides exactly by 12?
5. 5.Which of these numbers divides exactly by 4? (a) 7949 (b) 5361 (c) 8793 (d) 2720
6. 6.What is the smallest number you must add to 502 so that it divides exactly by 13?
7. 7.What is the smallest number you must add to 325 so that it divides exactly by 3?
8. 8.How many factors does 63 have?
9. 9.What is the smallest number you must add to 293 so that it divides exactly by 9?
10. 10.Which of these numbers divides exactly by 6? (a) 1468 (b) 7592 (c) 3753 (d) 9480
11. 11.Which of these numbers divides exactly by 6? (a) 9905 (b) 2032 (c) 6606 (d) 7378
12. 12.How many factors does 93 have?
13. 13.What is the smallest number you must add to 760 so that it divides exactly by 6?
14. 14.How many factors does 50 have?
15. 15.How many factors does 47 have?
16. 16.What is the smallest number you must take away from 624 so that it divides exactly by 7?
17. 17.How many factors does 58 have?
18. 18.How many factors does 25 have?
19. 19.What is the smallest number you must add to 838 so that it divides exactly by 11?
20. 20.What is the smallest number you must take away from 271 so that it divides exactly by 4?
21. 21.Which of these numbers divides exactly by 8? (a) 9257 (b) 1708 (c) 5874 (d) 6800
22. 22.Which of these numbers divides exactly by 6? (a) 3172 (b) 8914 (c) 4800 (d) 9879
23. 23.What is the smallest number you must take away from 310 so that it divides exactly by 8?
24. 24.What is the smallest number you must take away from 108 so that it divides exactly by 11?
25. 25.What is the smallest number you must take away from 156 so that it divides exactly by 7?
26. 26.How many factors does 64 have?
27. 27.How many factors does 16 have?
28. 28.What is the smallest number you must add to 228 so that it divides exactly by 7?
29. 29.What is the smallest number you must add to 847 so that it divides exactly by 13?
30. 30.What is the smallest number you must add to 107 so that it divides exactly by 13?
31. 31.Which of these numbers divides exactly by 9? (a) 3590 (b) 1560 (c) 1361 (d) 3699
32. 32.Which of these numbers divides exactly by 8? (a) 2398 (b) 2840 (c) 5635 (d) 1345
33. 33.What is the smallest number you must add to 722 so that it divides exactly by 11?
34. 34.What is the smallest number you must add to 442 so that it divides exactly by 7?
35. 35.What is the smallest number you must add to 579 so that it divides exactly by 13?
36. 36.What is the smallest number you must add to 631 so that it divides exactly by 4?
37. 37.What is the smallest number you must take away from 476 so that it divides exactly by 3?
38. 38.What is the smallest number you must add to 840 so that it divides exactly by 9?
39. 39.What is the smallest number you must add to 483 so that it divides exactly by 11?
40. 40.What is the smallest number you must take away from 479 so that it divides exactly by 9?

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