Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 76 · 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 194 so that it divides exactly by 11?
2. 2.What is the smallest number you must take away from 647 so that it divides exactly by 6?
3. 3.Which of these numbers divides exactly by 11? (a) 3151 (b) 1188 (c) 8896 (d) 1227
4. 4.How many factors does 20 have?
5. 5.What is the smallest number you must add to 966 so that it divides exactly by 4?
6. 6.How many factors does 23 have?
7. 7.How many factors does 65 have?
8. 8.How many factors does 31 have?
9. 9.What is the smallest number you must take away from 610 so that it divides exactly by 12?
10. 10.What is the smallest number you must take away from 353 so that it divides exactly by 9?
11. 11.What is the smallest number you must add to 857 so that it divides exactly by 9?
12. 12.How many factors does 79 have?
13. 13.Which of these numbers divides exactly by 6? (a) 8667 (b) 5261 (c) 4242 (d) 9961
14. 14.How many factors does 68 have?
15. 15.What is the smallest number you must take away from 842 so that it divides exactly by 3?
16. 16.Which of these numbers divides exactly by 6? (a) 2230 (b) 5714 (c) 1236 (d) 6512
17. 17.How many factors does 40 have?
18. 18.What is the smallest number you must add to 682 so that it divides exactly by 13?
19. 19.How many factors does 49 have?
20. 20.What is the smallest number you must add to 161 so that it divides exactly by 8?
21. 21.What is the smallest number you must add to 123 so that it divides exactly by 6?
22. 22.Which of these numbers divides exactly by 3? (a) 3808 (b) 2009 (c) 2839 (d) 2082
23. 23.What is the smallest number you must add to 296 so that it divides exactly by 11?
24. 24.How many factors does 26 have?
25. 25.What is the smallest number you must take away from 129 so that it divides exactly by 13?
26. 26.What is the smallest number you must add to 630 so that it divides exactly by 4?
27. 27.Which of these numbers divides exactly by 3? (a) 4625 (b) 1189 (c) 6989 (d) 9762
28. 28.What is the smallest number you must take away from 778 so that it divides exactly by 3?
29. 29.What is the smallest number you must add to 363 so that it divides exactly by 9?
30. 30.How many factors does 35 have?
31. 31.What is the smallest number you must add to 402 so that it divides exactly by 11?
32. 32.Which of these numbers divides exactly by 3? (a) 4204 (b) 4712 (c) 6056 (d) 8562
33. 33.What is the smallest number you must take away from 269 so that it divides exactly by 3?
34. 34.What is the smallest number you must add to 251 so that it divides exactly by 4?
35. 35.What is the smallest number you must take away from 329 so that it divides exactly by 6?
36. 36.Which of these numbers divides exactly by 9? (a) 9828 (b) 3542 (c) 6355 (d) 8193
37. 37.How many factors does 46 have?
38. 38.How many factors does 97 have?
39. 39.Which of these numbers divides exactly by 4? (a) 6058 (b) 6213 (c) 5366 (d) 5028
40. 40.What is the smallest number you must take away from 701 so that it divides exactly by 13?

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