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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 551 · 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 189870 divisible by 30?
  2. 2.Is 10374 divisible by 7?
  3. 3.Is 9364 divisible by 8?
  4. 4.Is 101878 divisible by 19?
  5. 5.Is 4256 divisible by 6?
  6. 6.Is 9600 divisible by 3?
  7. 7.Is 73569 divisible by 19?
  8. 8.Is 104856 divisible by 24?
  9. 9.Is 31963 divisible by 17?
  10. 10.Is 6211 divisible by 7?
  11. 11.Is 12051 divisible by 3?
  12. 12.Is 25162 divisible by 23?
  13. 13.Is 36949 divisible by 6?
  14. 14.Is 11306 divisible by 13?
  15. 15.Is 77324 divisible by 15?
  16. 16.Is 594 divisible by 5?
  17. 17.Is 94230 divisible by 18?
  18. 18.Is 18366 divisible by 3?
  19. 19.Is 5939 divisible by 4?
  20. 20.Is 3889 divisible by 6?
  21. 21.Is 1550 divisible by 13?
  22. 22.Is 98775 divisible by 29?
  23. 23.Is 95174 divisible by 23?
  24. 24.Is 151020 divisible by 23?
  25. 25.Is 78690 divisible by 15?
  26. 26.Is 2320 divisible by 5?
  27. 27.Is 16443 divisible by 29?
  28. 28.Is 55854 divisible by 19?
  29. 29.Is 1152 divisible by 12?
  30. 30.Is 97211 divisible by 30?
  31. 31.Is 13632 divisible by 12?
  32. 32.Is 34780 divisible by 6?
  33. 33.Is 59671 divisible by 19?
  34. 34.Is 80388 divisible by 15?
  35. 35.Is 89302 divisible by 20?
  36. 36.Is 102539 divisible by 18?
  37. 37.Is 50151 divisible by 12?
  38. 38.Is 78335 divisible by 12?
  39. 39.Is 55695 divisible by 15?
  40. 40.Is 20494 divisible by 23?

Answer key

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

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