Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 278 · 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 191 so that it divides exactly by 13?
2. 2.What is the smallest number you must add to 678 so that it divides exactly by 12?
3. 3.What is the smallest number you must add to 299 so that it divides exactly by 11?
4. 4.What is the smallest number you must take away from 726 so that it divides exactly by 12?
5. 5.How many factors does 100 have?
6. 6.What is the smallest number you must add to 861 so that it divides exactly by 12?
7. 7.Which of these numbers divides exactly by 3? (a) 3826 (b) 1155 (c) 2867 (d) 8914
8. 8.How many factors does 90 have?
9. 9.What is the smallest number you must add to 489 so that it divides exactly by 4?
10. 10.What is the smallest number you must take away from 749 so that it divides exactly by 3?
11. 11.What is the smallest number you must add to 802 so that it divides exactly by 12?
12. 12.Which of these numbers divides exactly by 11? (a) 4182 (b) 5859 (c) 6853 (d) 4877
13. 13.How many factors does 38 have?
14. 14.Which of these numbers divides exactly by 6? (a) 3959 (b) 8609 (c) 6587 (d) 9870
15. 15.What is the smallest number you must add to 571 so that it divides exactly by 8?
16. 16.How many factors does 51 have?
17. 17.What is the smallest number you must take away from 251 so that it divides exactly by 12?
18. 18.What is the smallest number you must take away from 200 so that it divides exactly by 11?
19. 19.What is the smallest number you must take away from 697 so that it divides exactly by 13?
20. 20.What is the smallest number you must add to 313 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 125 so that it divides exactly by 7?
22. 22.What is the smallest number you must take away from 253 so that it divides exactly by 13?
23. 23.How many factors does 25 have?
24. 24.How many factors does 54 have?
25. 25.What is the smallest number you must take away from 625 so that it divides exactly by 7?
26. 26.Which of these numbers divides exactly by 6? (a) 9151 (b) 6979 (c) 3576 (d) 9596
27. 27.How many factors does 73 have?
28. 28.What is the smallest number you must take away from 346 so that it divides exactly by 8?
29. 29.Which of these numbers divides exactly by 4? (a) 7467 (b) 8381 (c) 1064 (d) 8198
30. 30.Which of these numbers divides exactly by 8? (a) 6628 (b) 8216 (c) 4225 (d) 1441
31. 31.What is the smallest number you must add to 176 so that it divides exactly by 7?
32. 32.What is the smallest number you must add to 672 so that it divides exactly by 13?
33. 33.What is the smallest number you must take away from 766 so that it divides exactly by 8?
34. 34.How many factors does 35 have?
35. 35.What is the smallest number you must take away from 179 so that it divides exactly by 6?
36. 36.How many factors does 45 have?
37. 37.Which of these numbers divides exactly by 4? (a) 9147 (b) 6857 (c) 3112 (d) 8723
38. 38.Which of these numbers divides exactly by 4? (a) 2797 (b) 1214 (c) 1890 (d) 3316
39. 39.Which of these numbers divides exactly by 4? (a) 9586 (b) 6831 (c) 8074 (d) 4524
40. 40.How many factors does 81 have?

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