Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 253 · 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 374 so that it divides exactly by 3?
2. 2.What is the smallest number you must take away from 503 so that it divides exactly by 12?
3. 3.Which of these numbers divides exactly by 8? (a) 6508 (b) 3822 (c) 9136 (d) 7675
4. 4.Which of these numbers divides exactly by 4? (a) 5830 (b) 8031 (c) 6750 (d) 7480
5. 5.Which of these numbers divides exactly by 4? (a) 5212 (b) 2246 (c) 6366 (d) 8467
6. 6.What is the smallest number you must add to 571 so that it divides exactly by 13?
7. 7.What is the smallest number you must add to 129 so that it divides exactly by 9?
8. 8.Which of these numbers divides exactly by 6? (a) 9740 (b) 7750 (c) 6678 (d) 3081
9. 9.How many factors does 34 have?
10. 10.What is the smallest number you must add to 448 so that it divides exactly by 11?
11. 11.What is the smallest number you must take away from 131 so that it divides exactly by 3?
12. 12.What is the smallest number you must add to 674 so that it divides exactly by 7?
13. 13.What is the smallest number you must add to 971 so that it divides exactly by 12?
14. 14.How many factors does 51 have?
15. 15.How many factors does 33 have?
16. 16.Which of these numbers divides exactly by 4? (a) 8871 (b) 9504 (c) 7951 (d) 4586
17. 17.How many factors does 25 have?
18. 18.How many factors does 72 have?
19. 19.Which of these numbers divides exactly by 6? (a) 2429 (b) 5516 (c) 3259 (d) 9828
20. 20.What is the smallest number you must take away from 914 so that it divides exactly by 4?
21. 21.How many factors does 32 have?
22. 22.What is the smallest number you must add to 886 so that it divides exactly by 4?
23. 23.What is the smallest number you must add to 470 so that it divides exactly by 12?
24. 24.What is the smallest number you must take away from 592 so that it divides exactly by 13?
25. 25.What is the smallest number you must take away from 399 so that it divides exactly by 6?
26. 26.What is the smallest number you must take away from 326 so that it divides exactly by 6?
27. 27.What is the smallest number you must add to 766 so that it divides exactly by 6?
28. 28.What is the smallest number you must add to 827 so that it divides exactly by 6?
29. 29.How many factors does 30 have?
30. 30.What is the smallest number you must add to 313 so that it divides exactly by 9?
31. 31.Which of these numbers divides exactly by 11? (a) 8712 (b) 6188 (c) 4704 (d) 6630
32. 32.Which of these numbers divides exactly by 6? (a) 4494 (b) 1526 (c) 7144 (d) 2107
33. 33.What is the smallest number you must add to 344 so that it divides exactly by 11?
34. 34.What is the smallest number you must take away from 739 so that it divides exactly by 8?
35. 35.How many factors does 17 have?
36. 36.What is the smallest number you must take away from 213 so that it divides exactly by 8?
37. 37.Which of these numbers divides exactly by 6? (a) 1879 (b) 3297 (c) 1979 (d) 4302
38. 38.How many factors does 75 have?
39. 39.What is the smallest number you must take away from 903 so that it divides exactly by 6?
40. 40.How many factors does 26 have?

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