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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 836 · 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 30810 divisible by 5?
  2. 2.Is 17152 divisible by 3?
  3. 3.Is 11453 divisible by 13?
  4. 4.Is 64440 divisible by 18?
  5. 5.Is 22173 divisible by 19?
  6. 6.Is 19968 divisible by 4?
  7. 7.Is 171390 divisible by 30?
  8. 8.Is 42135 divisible by 11?
  9. 9.Is 86490 divisible by 15?
  10. 10.Is 3721 divisible by 9?
  11. 11.Is 8212 divisible by 4?
  12. 12.Is 16830 divisible by 5?
  13. 13.Is 46920 divisible by 8?
  14. 14.Is 9078 divisible by 5?
  15. 15.Is 8369 divisible by 6?
  16. 16.Is 45467 divisible by 11?
  17. 17.Is 199096 divisible by 29?
  18. 18.Is 2988 divisible by 12?
  19. 19.Is 68776 divisible by 15?
  20. 20.Is 49793 divisible by 17?
  21. 21.Is 71056 divisible by 13?
  22. 22.Is 2947 divisible by 7?
  23. 23.Is 2638 divisible by 4?
  24. 24.Is 10325 divisible by 2?
  25. 25.Is 4012 divisible by 2?
  26. 26.Is 80296 divisible by 12?
  27. 27.Is 54450 divisible by 18?
  28. 28.Is 30690 divisible by 9?
  29. 29.Is 44145 divisible by 15?
  30. 30.Is 68437 divisible by 10?
  31. 31.Is 3778 divisible by 10?
  32. 32.Is 41022 divisible by 18?
  33. 33.Is 10421 divisible by 3?
  34. 34.Is 108843 divisible by 19?
  35. 35.Is 317 divisible by 15?
  36. 36.Is 21688 divisible by 13?
  37. 37.Is 89297 divisible by 19?
  38. 38.Is 7410 divisible by 11?
  39. 39.Is 20166 divisible by 5?
  40. 40.Is 39714 divisible by 9?

Answer key

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

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