Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 267 · 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 868 so that it divides exactly by 13?
2. 2.What is the smallest number you must add to 766 so that it divides exactly by 9?
3. 3.Which of these numbers divides exactly by 4? (a) 6241 (b) 2974 (c) 9614 (d) 2856
4. 4.What is the smallest number you must add to 145 so that it divides exactly by 9?
5. 5.Which of these numbers divides exactly by 3? (a) 3155 (b) 4351 (c) 6636 (d) 6619
6. 6.How many factors does 15 have?
7. 7.How many factors does 39 have?
8. 8.What is the smallest number you must add to 563 so that it divides exactly by 13?
9. 9.What is the smallest number you must add to 397 so that it divides exactly by 13?
10. 10.What is the smallest number you must add to 653 so that it divides exactly by 11?
11. 11.What is the smallest number you must take away from 268 so that it divides exactly by 6?
12. 12.Which of these numbers divides exactly by 3? (a) 7237 (b) 2925 (c) 1424 (d) 4174
13. 13.What is the smallest number you must add to 623 so that it divides exactly by 6?
14. 14.Which of these numbers divides exactly by 11? (a) 9067 (b) 1022 (c) 5418 (d) 3245
15. 15.How many factors does 54 have?
16. 16.What is the smallest number you must take away from 278 so that it divides exactly by 9?
17. 17.What is the smallest number you must add to 193 so that it divides exactly by 9?
18. 18.How many factors does 33 have?
19. 19.How many factors does 21 have?
20. 20.Which of these numbers divides exactly by 3? (a) 5194 (b) 7446 (c) 4445 (d) 3959
21. 21.How many factors does 13 have?
22. 22.What is the smallest number you must add to 416 so that it divides exactly by 3?
23. 23.What is the smallest number you must add to 292 so that it divides exactly by 11?
24. 24.Which of these numbers divides exactly by 4? (a) 9521 (b) 3160 (c) 6709 (d) 8570
25. 25.What is the smallest number you must add to 527 so that it divides exactly by 11?
26. 26.What is the smallest number you must take away from 820 so that it divides exactly by 7?
27. 27.What is the smallest number you must add to 257 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 184 so that it divides exactly by 9?
29. 29.What is the smallest number you must add to 964 so that it divides exactly by 3?
30. 30.What is the smallest number you must take away from 453 so that it divides exactly by 7?
31. 31.Which of these numbers divides exactly by 3? (a) 5049 (b) 9464 (c) 2029 (d) 2902
32. 32.What is the smallest number you must take away from 305 so that it divides exactly by 9?
33. 33.Which of these numbers divides exactly by 3? (a) 7579 (b) 3420 (c) 8236 (d) 1664
34. 34.What is the smallest number you must take away from 947 so that it divides exactly by 4?
35. 35.Which of these numbers divides exactly by 3? (a) 2978 (b) 4739 (c) 6477 (d) 2836
36. 36.What is the smallest number you must add to 338 so that it divides exactly by 6?
37. 37.What is the smallest number you must add to 802 so that it divides exactly by 7?
38. 38.Which of these numbers divides exactly by 3? (a) 5179 (b) 7880 (c) 6720 (d) 7567
39. 39.What is the smallest number you must add to 658 so that it divides exactly by 3?
40. 40.How many factors does 27 have?

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