Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 65 · 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 take away from 896 so that it divides exactly by 3?
2. 2.What is the smallest number you must add to 820 so that it divides exactly by 7?
3. 3.How many factors does 33 have?
4. 4.Which of these numbers divides exactly by 4? (a) 6930 (b) 4046 (c) 5708 (d) 6399
5. 5.How many factors does 98 have?
6. 6.How many factors does 50 have?
7. 7.What is the smallest number you must take away from 518 so that it divides exactly by 12?
8. 8.Which of these numbers divides exactly by 11? (a) 5017 (b) 8184 (c) 2039 (d) 6132
9. 9.What is the smallest number you must take away from 683 so that it divides exactly by 6?
10. 10.Which of these numbers divides exactly by 3? (a) 8720 (b) 2881 (c) 7332 (d) 1877
11. 11.Which of these numbers divides exactly by 4? (a) 1237 (b) 7312 (c) 9814 (d) 2127
12. 12.How many factors does 67 have?
13. 13.Which of these numbers divides exactly by 6? (a) 1373 (b) 3578 (c) 2610 (d) 5927
14. 14.How many factors does 65 have?
15. 15.What is the smallest number you must take away from 794 so that it divides exactly by 7?
16. 16.What is the smallest number you must add to 838 so that it divides exactly by 13?
17. 17.What is the smallest number you must add to 188 so that it divides exactly by 11?
18. 18.How many factors does 28 have?
19. 19.Which of these numbers divides exactly by 9? (a) 2406 (b) 6956 (c) 1404 (d) 9933
20. 20.Which of these numbers divides exactly by 6? (a) 5777 (b) 7725 (c) 2886 (d) 1395
21. 21.What is the smallest number you must add to 422 so that it divides exactly by 9?
22. 22.How many factors does 66 have?
23. 23.What is the smallest number you must add to 245 so that it divides exactly by 12?
24. 24.Which of these numbers divides exactly by 8? (a) 9670 (b) 9064 (c) 9932 (d) 7034
25. 25.How many factors does 52 have?
26. 26.What is the smallest number you must take away from 957 so that it divides exactly by 12?
27. 27.How many factors does 47 have?
28. 28.Which of these numbers divides exactly by 9? (a) 2827 (b) 2293 (c) 4212 (d) 8176
29. 29.What is the smallest number you must take away from 857 so that it divides exactly by 3?
30. 30.What is the smallest number you must take away from 208 so that it divides exactly by 6?
31. 31.How many factors does 38 have?
32. 32.Which of these numbers divides exactly by 8? (a) 2841 (b) 9000 (c) 7445 (d) 3383
33. 33.Which of these numbers divides exactly by 6? (a) 3900 (b) 8522 (c) 1742 (d) 9097
34. 34.What is the smallest number you must take away from 145 so that it divides exactly by 8?
35. 35.Which of these numbers divides exactly by 8? (a) 8567 (b) 5424 (c) 9586 (d) 7319
36. 36.What is the smallest number you must add to 643 so that it divides exactly by 9?
37. 37.Which of these numbers divides exactly by 9? (a) 3020 (b) 3721 (c) 4988 (d) 7497
38. 38.Which of these numbers divides exactly by 11? (a) 3140 (b) 4620 (c) 7087 (d) 1844
39. 39.What is the smallest number you must take away from 532 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 524 so that it divides exactly by 6?

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