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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 439 · 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 37724 divisible by 23?
  2. 2.Is 204100 divisible by 30?
  3. 3.Is 19332 divisible by 9?
  4. 4.Is 54318 divisible by 17?
  5. 5.Is 18514 divisible by 10?
  6. 6.Is 4096 divisible by 8?
  7. 7.Is 87750 divisible by 15?
  8. 8.Is 21570 divisible by 6?
  9. 9.Is 36839 divisible by 8?
  10. 10.Is 72030 divisible by 30?
  11. 11.Is 197152 divisible by 29?
  12. 12.Is 84361 divisible by 29?
  13. 13.Is 5936 divisible by 3?
  14. 14.Is 46600 divisible by 20?
  15. 15.Is 759 divisible by 5?
  16. 16.Is 47307 divisible by 24?
  17. 17.Is 23661 divisible by 11?
  18. 18.Is 1152 divisible by 8?
  19. 19.Is 14889 divisible by 7?
  20. 20.Is 129457 divisible by 30?
  21. 21.Is 10992 divisible by 2?
  22. 22.Is 20696 divisible by 15?
  23. 23.Is 22446 divisible by 9?
  24. 24.Is 4750 divisible by 10?
  25. 25.Is 47640 divisible by 19?
  26. 26.Is 20710 divisible by 10?
  27. 27.Is 3402 divisible by 2?
  28. 28.Is 27523 divisible by 9?
  29. 29.Is 32228 divisible by 5?
  30. 30.Is 20834 divisible by 11?
  31. 31.Is 49944 divisible by 8?
  32. 32.Is 18584 divisible by 7?
  33. 33.Is 1278 divisible by 6?
  34. 34.Is 8400 divisible by 20?
  35. 35.Is 5988 divisible by 4?
  36. 36.Is 113896 divisible by 23?
  37. 37.Is 5520 divisible by 12?
  38. 38.Is 32949 divisible by 6?
  39. 39.Is 132283 divisible by 23?
  40. 40.Is 31130 divisible by 8?

Answer key

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

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