Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 171 · 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.How many factors does 86 have?
2. 2.What is the smallest number you must take away from 705 so that it divides exactly by 6?
3. 3.Which of these numbers divides exactly by 4? (a) 8915 (b) 6668 (c) 8037 (d) 6111
4. 4.What is the smallest number you must add to 435 so that it divides exactly by 11?
5. 5.Which of these numbers divides exactly by 6? (a) 4846 (b) 5419 (c) 9871 (d) 2400
6. 6.What is the smallest number you must add to 105 so that it divides exactly by 12?
7. 7.What is the smallest number you must add to 434 so that it divides exactly by 6?
8. 8.What is the smallest number you must add to 239 so that it divides exactly by 7?
9. 9.What is the smallest number you must add to 250 so that it divides exactly by 8?
10. 10.Which of these numbers divides exactly by 6? (a) 1981 (b) 1445 (c) 3467 (d) 7092
11. 11.What is the smallest number you must add to 431 so that it divides exactly by 6?
12. 12.What is the smallest number you must take away from 133 so that it divides exactly by 6?
13. 13.How many factors does 39 have?
14. 14.How many factors does 98 have?
15. 15.Which of these numbers divides exactly by 8? (a) 2286 (b) 8630 (c) 3015 (d) 6696
16. 16.What is the smallest number you must add to 778 so that it divides exactly by 11?
17. 17.Which of these numbers divides exactly by 4? (a) 2558 (b) 1640 (c) 9722 (d) 8706
18. 18.What is the smallest number you must add to 452 so that it divides exactly by 6?
19. 19.How many factors does 56 have?
20. 20.Which of these numbers divides exactly by 3? (a) 5728 (b) 3925 (c) 5619 (d) 6364
21. 21.What is the smallest number you must add to 187 so that it divides exactly by 9?
22. 22.What is the smallest number you must add to 817 so that it divides exactly by 8?
23. 23.Which of these numbers divides exactly by 8? (a) 1016 (b) 5851 (c) 8057 (d) 1209
24. 24.How many factors does 85 have?
25. 25.What is the smallest number you must add to 557 so that it divides exactly by 12?
26. 26.What is the smallest number you must add to 664 so that it divides exactly by 12?
27. 27.Which of these numbers divides exactly by 6? (a) 9607 (b) 3091 (c) 5428 (d) 7488
28. 28.How many factors does 26 have?
29. 29.Which of these numbers divides exactly by 3? (a) 9294 (b) 9173 (c) 4487 (d) 2920
30. 30.What is the smallest number you must add to 426 so that it divides exactly by 4?
31. 31.What is the smallest number you must add to 799 so that it divides exactly by 9?
32. 32.How many factors does 62 have?
33. 33.What is the smallest number you must take away from 322 so that it divides exactly by 11?
34. 34.How many factors does 41 have?
35. 35.What is the smallest number you must add to 188 so that it divides exactly by 12?
36. 36.How many factors does 40 have?
37. 37.What is the smallest number you must take away from 820 so that it divides exactly by 12?
38. 38.What is the smallest number you must add to 309 so that it divides exactly by 9?
39. 39.Which of these numbers divides exactly by 4? (a) 1681 (b) 9525 (c) 2778 (d) 3012
40. 40.What is the smallest number you must add to 371 so that it divides exactly by 8?

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