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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 794 · 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 104662 divisible by 15?
  2. 2.Is 66713 divisible by 23?
  3. 3.Is 27860 divisible by 24?
  4. 4.Is 9523 divisible by 6?
  5. 5.Is 35060 divisible by 11?
  6. 6.Is 11592 divisible by 6?
  7. 7.Is 42319 divisible by 11?
  8. 8.Is 8592 divisible by 12?
  9. 9.Is 22986 divisible by 7?
  10. 10.Is 28278 divisible by 6?
  11. 11.Is 61213 divisible by 20?
  12. 12.Is 7955 divisible by 5?
  13. 13.Is 108714 divisible by 19?
  14. 14.Is 23693 divisible by 19?
  15. 15.Is 73378 divisible by 19?
  16. 16.Is 192715 divisible by 30?
  17. 17.Is 53440 divisible by 10?
  18. 18.Is 16707 divisible by 3?
  19. 19.Is 10327 divisible by 8?
  20. 20.Is 34010 divisible by 19?
  21. 21.Is 32378 divisible by 6?
  22. 22.Is 47343 divisible by 23?
  23. 23.Is 6237 divisible by 9?
  24. 24.Is 58639 divisible by 11?
  25. 25.Is 23738 divisible by 10?
  26. 26.Is 21615 divisible by 5?
  27. 27.Is 1755 divisible by 15?
  28. 28.Is 5520 divisible by 10?
  29. 29.Is 3998 divisible by 8?
  30. 30.Is 52345 divisible by 29?
  31. 31.Is 17988 divisible by 3?
  32. 32.Is 61030 divisible by 12?
  33. 33.Is 862 divisible by 20?
  34. 34.Is 73318 divisible by 30?
  35. 35.Is 9612 divisible by 18?
  36. 36.Is 26944 divisible by 19?
  37. 37.Is 2136 divisible by 2?
  38. 38.Is 8997 divisible by 12?
  39. 39.Is 1254 divisible by 3?
  40. 40.Is 38040 divisible by 20?

Answer key

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

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