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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 915 · 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 19176 divisible by 3?
  2. 2.Is 149661 divisible by 23?
  3. 3.Is 47410 divisible by 11?
  4. 4.Is 104461 divisible by 20?
  5. 5.Is 26617 divisible by 5?
  6. 6.Is 74681 divisible by 23?
  7. 7.Is 24653 divisible by 13?
  8. 8.Is 166170 divisible by 30?
  9. 9.Is 1546 divisible by 4?
  10. 10.Is 29820 divisible by 15?
  11. 11.Is 30084 divisible by 6?
  12. 12.Is 899 divisible by 5?
  13. 13.Is 84584 divisible by 18?
  14. 14.Is 5786 divisible by 12?
  15. 15.Is 22992 divisible by 24?
  16. 16.Is 17405 divisible by 3?
  17. 17.Is 49369 divisible by 11?
  18. 18.Is 54403 divisible by 20?
  19. 19.Is 67980 divisible by 17?
  20. 20.Is 39078 divisible by 13?
  21. 21.Is 7960 divisible by 10?
  22. 22.Is 36109 divisible by 8?
  23. 23.Is 18436 divisible by 11?
  24. 24.Is 13568 divisible by 8?
  25. 25.Is 8376 divisible by 12?
  26. 26.Is 61812 divisible by 11?
  27. 27.Is 30750 divisible by 8?
  28. 28.Is 1711 divisible by 3?
  29. 29.Is 1330 divisible by 3?
  30. 30.Is 2397 divisible by 3?
  31. 31.Is 23400 divisible by 12?
  32. 32.Is 30215 divisible by 5?
  33. 33.Is 9840 divisible by 6?
  34. 34.Is 43176 divisible by 11?
  35. 35.Is 14526 divisible by 5?
  36. 36.Is 98690 divisible by 23?
  37. 37.Is 91156 divisible by 24?
  38. 38.Is 12509 divisible by 4?
  39. 39.Is 38448 divisible by 8?
  40. 40.Is 27104 divisible by 4?

Answer key

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

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