Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 55 · 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 830 so that it divides exactly by 11?
2. 2.What is the smallest number you must take away from 454 so that it divides exactly by 7?
3. 3.What is the smallest number you must add to 961 so that it divides exactly by 11?
4. 4.What is the smallest number you must take away from 453 so that it divides exactly by 13?
5. 5.How many factors does 67 have?
6. 6.What is the smallest number you must add to 335 so that it divides exactly by 6?
7. 7.What is the smallest number you must take away from 373 so that it divides exactly by 13?
8. 8.What is the smallest number you must add to 289 so that it divides exactly by 3?
9. 9.Which of these numbers divides exactly by 11? (a) 3599 (b) 5492 (c) 8392 (d) 3124
10. 10.Which of these numbers divides exactly by 4? (a) 3077 (b) 5390 (c) 2789 (d) 9220
11. 11.What is the smallest number you must take away from 950 so that it divides exactly by 4?
12. 12.Which of these numbers divides exactly by 11? (a) 7328 (b) 6342 (c) 4332 (d) 2343
13. 13.How many factors does 91 have?
14. 14.Which of these numbers divides exactly by 4? (a) 4804 (b) 2211 (c) 2049 (d) 6657
15. 15.How many factors does 92 have?
16. 16.Which of these numbers divides exactly by 3? (a) 3451 (b) 6925 (c) 2660 (d) 5559
17. 17.How many factors does 12 have?
18. 18.How many factors does 94 have?
19. 19.What is the smallest number you must add to 994 so that it divides exactly by 4?
20. 20.What is the smallest number you must add to 169 so that it divides exactly by 3?
21. 21.What is the smallest number you must add to 741 so that it divides exactly by 7?
22. 22.Which of these numbers divides exactly by 3? (a) 9054 (b) 9871 (c) 2507 (d) 1697
23. 23.How many factors does 27 have?
24. 24.What is the smallest number you must take away from 292 so that it divides exactly by 12?
25. 25.What is the smallest number you must add to 404 so that it divides exactly by 3?
26. 26.What is the smallest number you must take away from 164 so that it divides exactly by 7?
27. 27.What is the smallest number you must add to 234 so that it divides exactly by 11?
28. 28.What is the smallest number you must add to 603 so that it divides exactly by 11?
29. 29.Which of these numbers divides exactly by 3? (a) 4754 (b) 1611 (c) 2318 (d) 9577
30. 30.What is the smallest number you must add to 198 so that it divides exactly by 7?
31. 31.Which of these numbers divides exactly by 4? (a) 6815 (b) 9972 (c) 3766 (d) 6974
32. 32.How many factors does 59 have?
33. 33.How many factors does 99 have?
34. 34.How many factors does 75 have?
35. 35.What is the smallest number you must take away from 401 so that it divides exactly by 4?
36. 36.What is the smallest number you must take away from 800 so that it divides exactly by 9?
37. 37.How many factors does 93 have?
38. 38.Which of these numbers divides exactly by 4? (a) 3513 (b) 1180 (c) 5733 (d) 6553
39. 39.What is the smallest number you must add to 225 so that it divides exactly by 6?
40. 40.How many factors does 20 have?

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