Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 124 · 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 475 so that it divides exactly by 8?
2. 2.How many factors does 47 have?
3. 3.Which of these numbers divides exactly by 3? (a) 6230 (b) 9989 (c) 7476 (d) 1532
4. 4.What is the smallest number you must add to 390 so that it divides exactly by 4?
5. 5.What is the smallest number you must add to 269 so that it divides exactly by 3?
6. 6.How many factors does 35 have?
7. 7.What is the smallest number you must add to 544 so that it divides exactly by 11?
8. 8.What is the smallest number you must take away from 383 so that it divides exactly by 8?
9. 9.Which of these numbers divides exactly by 9? (a) 4158 (b) 5060 (c) 5900 (d) 1945
10. 10.What is the smallest number you must take away from 990 so that it divides exactly by 12?
11. 11.What is the smallest number you must take away from 774 so that it divides exactly by 8?
12. 12.What is the smallest number you must add to 580 so that it divides exactly by 12?
13. 13.How many factors does 73 have?
14. 14.Which of these numbers divides exactly by 6? (a) 6768 (b) 4351 (c) 3549 (d) 3063
15. 15.How many factors does 81 have?
16. 16.How many factors does 99 have?
17. 17.What is the smallest number you must take away from 999 so that it divides exactly by 13?
18. 18.What is the smallest number you must take away from 806 so that it divides exactly by 6?
19. 19.What is the smallest number you must add to 497 so that it divides exactly by 6?
20. 20.How many factors does 39 have?
21. 21.What is the smallest number you must add to 310 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 137 so that it divides exactly by 4?
23. 23.What is the smallest number you must add to 758 so that it divides exactly by 9?
24. 24.Which of these numbers divides exactly by 4? (a) 9921 (b) 2420 (c) 1246 (d) 7986
25. 25.What is the smallest number you must take away from 425 so that it divides exactly by 9?
26. 26.How many factors does 33 have?
27. 27.What is the smallest number you must add to 862 so that it divides exactly by 3?
28. 28.How many factors does 43 have?
29. 29.What is the smallest number you must add to 575 so that it divides exactly by 11?
30. 30.How many factors does 46 have?
31. 31.What is the smallest number you must add to 537 so that it divides exactly by 9?
32. 32.Which of these numbers divides exactly by 8? (a) 6077 (b) 8424 (c) 6585 (d) 4533
33. 33.How many factors does 38 have?
34. 34.Which of these numbers divides exactly by 9? (a) 1206 (b) 9289 (c) 1447 (d) 1101
35. 35.What is the smallest number you must take away from 835 so that it divides exactly by 3?
36. 36.What is the smallest number you must take away from 883 so that it divides exactly by 6?
37. 37.Which of these numbers divides exactly by 8? (a) 8332 (b) 7381 (c) 4592 (d) 4607
38. 38.Which of these numbers divides exactly by 6? (a) 1295 (b) 1542 (c) 7034 (d) 4049
39. 39.What is the smallest number you must take away from 256 so that it divides exactly by 12?
40. 40.What is the smallest number you must take away from 856 so that it divides exactly by 6?

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