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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 50 · 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 40413 divisible by 7?
  2. 2.Is 27139 divisible by 7?
  3. 3.Is 25762 divisible by 11?
  4. 4.Is 1720 divisible by 20?
  5. 5.Is 169440 divisible by 30?
  6. 6.Is 7609 divisible by 3?
  7. 7.Is 195660 divisible by 30?
  8. 8.Is 8192 divisible by 4?
  9. 9.Is 109152 divisible by 24?
  10. 10.Is 111327 divisible by 17?
  11. 11.Is 122006 divisible by 23?
  12. 12.Is 3855 divisible by 4?
  13. 13.Is 16944 divisible by 4?
  14. 14.Is 1284 divisible by 3?
  15. 15.Is 136370 divisible by 23?
  16. 16.Is 1632 divisible by 4?
  17. 17.Is 1374 divisible by 5?
  18. 18.Is 54351 divisible by 13?
  19. 19.Is 4778 divisible by 3?
  20. 20.Is 111573 divisible by 23?
  21. 21.Is 26201 divisible by 19?
  22. 22.Is 67545 divisible by 19?
  23. 23.Is 28242 divisible by 5?
  24. 24.Is 3492 divisible by 12?
  25. 25.Is 14812 divisible by 9?
  26. 26.Is 43392 divisible by 7?
  27. 27.Is 133512 divisible by 24?
  28. 28.Is 42460 divisible by 20?
  29. 29.Is 59268 divisible by 12?
  30. 30.Is 43547 divisible by 24?
  31. 31.Is 83016 divisible by 18?
  32. 32.Is 49896 divisible by 18?
  33. 33.Is 223 divisible by 3?
  34. 34.Is 3559 divisible by 2?
  35. 35.Is 8969 divisible by 2?
  36. 36.Is 109620 divisible by 30?
  37. 37.Is 36467 divisible by 6?
  38. 38.Is 4447 divisible by 2?
  39. 39.Is 48432 divisible by 10?
  40. 40.Is 2638 divisible by 12?

Answer key

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

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