Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 152 · 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 569 so that it divides exactly by 9?
2. 2.What is the smallest number you must add to 977 so that it divides exactly by 7?
3. 3.What is the smallest number you must add to 919 so that it divides exactly by 4?
4. 4.How many factors does 97 have?
5. 5.What is the smallest number you must add to 777 so that it divides exactly by 9?
6. 6.How many factors does 14 have?
7. 7.What is the smallest number you must take away from 739 so that it divides exactly by 8?
8. 8.What is the smallest number you must take away from 372 so that it divides exactly by 7?
9. 9.How many factors does 84 have?
10. 10.Which of these numbers divides exactly by 4? (a) 3090 (b) 3260 (c) 8597 (d) 6503
11. 11.What is the smallest number you must take away from 499 so that it divides exactly by 7?
12. 12.What is the smallest number you must take away from 668 so that it divides exactly by 6?
13. 13.How many factors does 19 have?
14. 14.What is the smallest number you must take away from 766 so that it divides exactly by 4?
15. 15.Which of these numbers divides exactly by 9? (a) 5808 (b) 8955 (c) 4862 (d) 2509
16. 16.Which of these numbers divides exactly by 9? (a) 6510 (b) 1422 (c) 8936 (d) 3845
17. 17.What is the smallest number you must add to 633 so that it divides exactly by 7?
18. 18.What is the smallest number you must take away from 178 so that it divides exactly by 13?
19. 19.Which of these numbers divides exactly by 3? (a) 6570 (b) 1483 (c) 4837 (d) 3374
20. 20.What is the smallest number you must add to 948 so that it divides exactly by 7?
21. 21.What is the smallest number you must take away from 716 so that it divides exactly by 3?
22. 22.What is the smallest number you must add to 556 so that it divides exactly by 11?
23. 23.Which of these numbers divides exactly by 3? (a) 5497 (b) 2289 (c) 4472 (d) 4987
24. 24.How many factors does 68 have?
25. 25.What is the smallest number you must take away from 259 so that it divides exactly by 4?
26. 26.How many factors does 35 have?
27. 27.What is the smallest number you must add to 214 so that it divides exactly by 13?
28. 28.What is the smallest number you must take away from 974 so that it divides exactly by 8?
29. 29.How many factors does 40 have?
30. 30.What is the smallest number you must add to 365 so that it divides exactly by 4?
31. 31.How many factors does 99 have?
32. 32.What is the smallest number you must take away from 620 so that it divides exactly by 12?
33. 33.What is the smallest number you must take away from 363 so that it divides exactly by 13?
34. 34.How many factors does 26 have?
35. 35.How many factors does 66 have?
36. 36.What is the smallest number you must add to 731 so that it divides exactly by 6?
37. 37.How many factors does 41 have?
38. 38.What is the smallest number you must take away from 480 so that it divides exactly by 7?
39. 39.Which of these numbers divides exactly by 9? (a) 2803 (b) 7824 (c) 6622 (d) 3204
40. 40.What is the smallest number you must add to 909 so that it divides exactly by 7?

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