Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 258 · 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 255 so that it divides exactly by 7?
2. 2.Which of these numbers divides exactly by 8? (a) 7204 (b) 8542 (c) 5184 (d) 3887
3. 3.How many factors does 46 have?
4. 4.What is the smallest number you must take away from 857 so that it divides exactly by 13?
5. 5.What is the smallest number you must add to 343 so that it divides exactly by 4?
6. 6.How many factors does 51 have?
7. 7.What is the smallest number you must take away from 966 so that it divides exactly by 13?
8. 8.Which of these numbers divides exactly by 3? (a) 1241 (b) 6413 (c) 7825 (d) 9369
9. 9.How many factors does 64 have?
10. 10.Which of these numbers divides exactly by 9? (a) 9710 (b) 2052 (c) 9660 (d) 6106
11. 11.How many factors does 86 have?
12. 12.What is the smallest number you must take away from 988 so that it divides exactly by 11?
13. 13.Which of these numbers divides exactly by 8? (a) 1536 (b) 6715 (c) 1382 (d) 4615
14. 14.Which of these numbers divides exactly by 6? (a) 4629 (b) 2813 (c) 6354 (d) 3789
15. 15.Which of these numbers divides exactly by 3? (a) 7669 (b) 1635 (c) 6560 (d) 2893
16. 16.What is the smallest number you must take away from 922 so that it divides exactly by 12?
17. 17.How many factors does 67 have?
18. 18.Which of these numbers divides exactly by 8? (a) 9228 (b) 6419 (c) 7962 (d) 4416
19. 19.What is the smallest number you must add to 437 so that it divides exactly by 6?
20. 20.How many factors does 15 have?
21. 21.What is the smallest number you must add to 633 so that it divides exactly by 4?
22. 22.How many factors does 44 have?
23. 23.What is the smallest number you must add to 346 so that it divides exactly by 4?
24. 24.What is the smallest number you must add to 419 so that it divides exactly by 6?
25. 25.What is the smallest number you must take away from 747 so that it divides exactly by 8?
26. 26.What is the smallest number you must add to 467 so that it divides exactly by 12?
27. 27.What is the smallest number you must add to 193 so that it divides exactly by 4?
28. 28.Which of these numbers divides exactly by 6? (a) 4162 (b) 6084 (c) 7391 (d) 9237
29. 29.Which of these numbers divides exactly by 11? (a) 8877 (b) 5943 (c) 5078 (d) 7600
30. 30.What is the smallest number you must add to 411 so that it divides exactly by 8?
31. 31.Which of these numbers divides exactly by 4? (a) 4290 (b) 8828 (c) 5075 (d) 4359
32. 32.How many factors does 14 have?
33. 33.What is the smallest number you must take away from 267 so that it divides exactly by 11?
34. 34.How many factors does 96 have?
35. 35.Which of these numbers divides exactly by 11? (a) 8320 (b) 8803 (c) 4532 (d) 8990
36. 36.What is the smallest number you must take away from 518 so that it divides exactly by 4?
37. 37.How many factors does 90 have?
38. 38.Which of these numbers divides exactly by 4? (a) 9658 (b) 2154 (c) 4752 (d) 8666
39. 39.How many factors does 31 have?
40. 40.How many factors does 17 have?

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