Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 295 · 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 712 so that it divides exactly by 7?
2. 2.What is the smallest number you must take away from 646 so that it divides exactly by 6?
3. 3.What is the smallest number you must take away from 188 so that it divides exactly by 12?
4. 4.What is the smallest number you must take away from 883 so that it divides exactly by 9?
5. 5.Which of these numbers divides exactly by 8? (a) 4588 (b) 5590 (c) 2096 (d) 5684
6. 6.What is the smallest number you must take away from 266 so that it divides exactly by 8?
7. 7.What is the smallest number you must take away from 421 so that it divides exactly by 6?
8. 8.What is the smallest number you must add to 668 so that it divides exactly by 7?
9. 9.Which of these numbers divides exactly by 4? (a) 7539 (b) 8475 (c) 9434 (d) 1928
10. 10.What is the smallest number you must take away from 659 so that it divides exactly by 13?
11. 11.How many factors does 94 have?
12. 12.Which of these numbers divides exactly by 3? (a) 1311 (b) 8644 (c) 5654 (d) 1277
13. 13.What is the smallest number you must add to 838 so that it divides exactly by 12?
14. 14.What is the smallest number you must add to 171 so that it divides exactly by 12?
15. 15.What is the smallest number you must take away from 836 so that it divides exactly by 6?
16. 16.How many factors does 22 have?
17. 17.Which of these numbers divides exactly by 8? (a) 3204 (b) 2166 (c) 2575 (d) 8616
18. 18.Which of these numbers divides exactly by 8? (a) 4302 (b) 3080 (c) 9906 (d) 2965
19. 19.Which of these numbers divides exactly by 6? (a) 7967 (b) 3981 (c) 9396 (d) 7271
20. 20.How many factors does 91 have?
21. 21.How many factors does 68 have?
22. 22.What is the smallest number you must take away from 937 so that it divides exactly by 9?
23. 23.What is the smallest number you must take away from 100 so that it divides exactly by 3?
24. 24.What is the smallest number you must take away from 947 so that it divides exactly by 6?
25. 25.Which of these numbers divides exactly by 9? (a) 8439 (b) 6432 (c) 5947 (d) 7803
26. 26.Which of these numbers divides exactly by 3? (a) 6459 (b) 7973 (c) 2507 (d) 3551
27. 27.Which of these numbers divides exactly by 8? (a) 4123 (b) 3697 (c) 3240 (d) 9791
28. 28.How many factors does 85 have?
29. 29.What is the smallest number you must take away from 367 so that it divides exactly by 7?
30. 30.What is the smallest number you must add to 570 so that it divides exactly by 11?
31. 31.What is the smallest number you must take away from 203 so that it divides exactly by 6?
32. 32.How many factors does 14 have?
33. 33.What is the smallest number you must take away from 360 so that it divides exactly by 7?
34. 34.What is the smallest number you must add to 957 so that it divides exactly by 8?
35. 35.What is the smallest number you must take away from 124 so that it divides exactly by 7?
36. 36.How many factors does 63 have?
37. 37.Which of these numbers divides exactly by 4? (a) 4331 (b) 7980 (c) 7681 (d) 9529
38. 38.What is the smallest number you must add to 325 so that it divides exactly by 3?
39. 39.What is the smallest number you must add to 224 so that it divides exactly by 13?
40. 40.What is the smallest number you must take away from 191 so that it divides exactly by 12?

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