Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 223 · 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 3? (a) 9948 (b) 5176 (c) 1949 (d) 2795
2. 2.How many factors does 98 have?
3. 3.What is the smallest number you must take away from 777 so that it divides exactly by 12?
4. 4.Which of these numbers divides exactly by 9? (a) 7006 (b) 2046 (c) 9986 (d) 6966
5. 5.How many factors does 35 have?
6. 6.Which of these numbers divides exactly by 11? (a) 4409 (b) 7032 (c) 6138 (d) 2762
7. 7.What is the smallest number you must take away from 698 so that it divides exactly by 9?
8. 8.What is the smallest number you must take away from 158 so that it divides exactly by 6?
9. 9.Which of these numbers divides exactly by 3? (a) 8154 (b) 1537 (c) 9007 (d) 3838
10. 10.Which of these numbers divides exactly by 9? (a) 7757 (b) 4370 (c) 9036 (d) 2338
11. 11.How many factors does 72 have?
12. 12.What is the smallest number you must add to 454 so that it divides exactly by 12?
13. 13.What is the smallest number you must add to 402 so that it divides exactly by 9?
14. 14.What is the smallest number you must add to 391 so that it divides exactly by 8?
15. 15.What is the smallest number you must add to 148 so that it divides exactly by 13?
16. 16.Which of these numbers divides exactly by 4? (a) 7753 (b) 9763 (c) 8862 (d) 6192
17. 17.How many factors does 15 have?
18. 18.What is the smallest number you must take away from 806 so that it divides exactly by 8?
19. 19.Which of these numbers divides exactly by 6? (a) 5581 (b) 5531 (c) 4418 (d) 4176
20. 20.Which of these numbers divides exactly by 8? (a) 7221 (b) 3161 (c) 1281 (d) 7816
21. 21.How many factors does 36 have?
22. 22.Which of these numbers divides exactly by 6? (a) 9461 (b) 4091 (c) 5106 (d) 5555
23. 23.What is the smallest number you must take away from 907 so that it divides exactly by 4?
24. 24.What is the smallest number you must take away from 101 so that it divides exactly by 13?
25. 25.What is the smallest number you must take away from 125 so that it divides exactly by 4?
26. 26.What is the smallest number you must take away from 932 so that it divides exactly by 8?
27. 27.How many factors does 13 have?
28. 28.How many factors does 17 have?
29. 29.How many factors does 54 have?
30. 30.What is the smallest number you must take away from 124 so that it divides exactly by 12?
31. 31.What is the smallest number you must add to 811 so that it divides exactly by 8?
32. 32.How many factors does 47 have?
33. 33.How many factors does 19 have?
34. 34.How many factors does 78 have?
35. 35.What is the smallest number you must add to 344 so that it divides exactly by 11?
36. 36.What is the smallest number you must take away from 375 so that it divides exactly by 8?
37. 37.What is the smallest number you must add to 657 so that it divides exactly by 7?
38. 38.Which of these numbers divides exactly by 4? (a) 3597 (b) 7731 (c) 1420 (d) 1891
39. 39.What is the smallest number you must add to 259 so that it divides exactly by 4?
40. 40.What is the smallest number you must take away from 196 so that it divides exactly by 8?

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