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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 371 · 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 17146 divisible by 5?
  2. 2.Is 10560 divisible by 24?
  3. 3.Is 89136 divisible by 18?
  4. 4.Is 9551 divisible by 2?
  5. 5.Is 35161 divisible by 7?
  6. 6.Is 21195 divisible by 5?
  7. 7.Is 21399 divisible by 6?
  8. 8.Is 19163 divisible by 30?
  9. 9.Is 26275 divisible by 11?
  10. 10.Is 64457 divisible by 24?
  11. 11.Is 104518 divisible by 17?
  12. 12.Is 76009 divisible by 30?
  13. 13.Is 40090 divisible by 6?
  14. 14.Is 102051 divisible by 29?
  15. 15.Is 15612 divisible by 8?
  16. 16.Is 29790 divisible by 18?
  17. 17.Is 13607 divisible by 4?
  18. 18.Is 8352 divisible by 2?
  19. 19.Is 2767 divisible by 2?
  20. 20.Is 12280 divisible by 6?
  21. 21.Is 42777 divisible by 9?
  22. 22.Is 19812 divisible by 13?
  23. 23.Is 109463 divisible by 17?
  24. 24.Is 3915 divisible by 29?
  25. 25.Is 18012 divisible by 3?
  26. 26.Is 30053 divisible by 10?
  27. 27.Is 52401 divisible by 19?
  28. 28.Is 114440 divisible by 17?
  29. 29.Is 17480 divisible by 10?
  30. 30.Is 36449 divisible by 9?
  31. 31.Is 87154 divisible by 18?
  32. 32.Is 2208 divisible by 3?
  33. 33.Is 66192 divisible by 24?
  34. 34.Is 20713 divisible by 8?
  35. 35.Is 41346 divisible by 9?
  36. 36.Is 3412 divisible by 10?
  37. 37.Is 71946 divisible by 18?
  38. 38.Is 2700 divisible by 18?
  39. 39.Is 64040 divisible by 10?
  40. 40.Is 40651 divisible by 7?

Answer key

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

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