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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 114 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 61880 divisible by 20?
  2. 2.Is 19396 divisible by 11?
  3. 3.Is 38335 divisible by 18?
  4. 4.Is 74286 divisible by 13?
  5. 5.Is 50550 divisible by 15?
  6. 6.Is 5438 divisible by 2?
  7. 7.Is 39355 divisible by 10?
  8. 8.Is 24513 divisible by 4?
  9. 9.Is 16261 divisible by 15?
  10. 10.Is 22515 divisible by 7?
  11. 11.Is 89835 divisible by 15?
  12. 12.Is 10906 divisible by 8?
  13. 13.Is 44312 divisible by 8?
  14. 14.Is 36048 divisible by 6?
  15. 15.Is 64075 divisible by 30?
  16. 16.Is 1863 divisible by 3?
  17. 17.Is 37405 divisible by 7?
  18. 18.Is 29560 divisible by 11?
  19. 19.Is 39405 divisible by 15?
  20. 20.Is 11155 divisible by 5?
  21. 21.Is 3491 divisible by 10?
  22. 22.Is 152758 divisible by 23?
  23. 23.Is 105528 divisible by 23?
  24. 24.Is 134340 divisible by 20?
  25. 25.Is 61737 divisible by 13?
  26. 26.Is 6935 divisible by 7?
  27. 27.Is 59995 divisible by 13?
  28. 28.Is 28340 divisible by 20?
  29. 29.Is 20149 divisible by 4?
  30. 30.Is 2516 divisible by 4?
  31. 31.Is 101640 divisible by 30?
  32. 32.Is 30565 divisible by 24?
  33. 33.Is 20315 divisible by 19?
  34. 34.Is 7620 divisible by 7?
  35. 35.Is 145682 divisible by 23?
  36. 36.Is 154248 divisible by 24?
  37. 37.Is 146820 divisible by 30?
  38. 38.Is 107172 divisible by 29?
  39. 39.Is 145165 divisible by 24?
  40. 40.Is 3050 divisible by 9?

Answer key

  1. yes
  2. no
  3. no
  4. no
  5. yes
  6. yes
  7. no
  8. no
  9. no
  10. no
  11. yes
  12. no
  13. yes
  14. yes
  15. no
  16. yes
  17. no
  18. no
  19. yes
  20. yes
  21. no
  22. no
  23. no
  24. yes
  25. yes
  26. no
  27. yes
  28. yes
  29. no
  30. yes
  31. yes
  32. no
  33. no
  34. no
  35. yes
  36. yes
  37. yes
  38. no
  39. no
  40. no

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