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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 413 · 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 12887 divisible by 3?
  2. 2.Is 24621 divisible by 29?
  3. 3.Is 2045 divisible by 2?
  4. 4.Is 57215 divisible by 20?
  5. 5.Is 16976 divisible by 8?
  6. 6.Is 20743 divisible by 3?
  7. 7.Is 133561 divisible by 29?
  8. 8.Is 28325 divisible by 12?
  9. 9.Is 24219 divisible by 13?
  10. 10.Is 7068 divisible by 6?
  11. 11.Is 127155 divisible by 23?
  12. 12.Is 4354 divisible by 4?
  13. 13.Is 75870 divisible by 20?
  14. 14.Is 49495 divisible by 20?
  15. 15.Is 58509 divisible by 9?
  16. 16.Is 26078 divisible by 13?
  17. 17.Is 43363 divisible by 7?
  18. 18.Is 71088 divisible by 24?
  19. 19.Is 10019 divisible by 2?
  20. 20.Is 33795 divisible by 5?
  21. 21.Is 31664 divisible by 10?
  22. 22.Is 11239 divisible by 6?
  23. 23.Is 9888 divisible by 12?
  24. 24.Is 14686 divisible by 6?
  25. 25.Is 25213 divisible by 4?
  26. 26.Is 20340 divisible by 23?
  27. 27.Is 26477 divisible by 7?
  28. 28.Is 175620 divisible by 30?
  29. 29.Is 53605 divisible by 19?
  30. 30.Is 90558 divisible by 18?
  31. 31.Is 20561 divisible by 8?
  32. 32.Is 26149 divisible by 13?
  33. 33.Is 98070 divisible by 30?
  34. 34.Is 115329 divisible by 17?
  35. 35.Is 4411 divisible by 11?
  36. 36.Is 4607 divisible by 4?
  37. 37.Is 9005 divisible by 3?
  38. 38.Is 18949 divisible by 4?
  39. 39.Is 44959 divisible by 19?
  40. 40.Is 9577 divisible by 10?

Answer key

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

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