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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 646 · 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 44897 divisible by 9?
  2. 2.Is 12495 divisible by 15?
  3. 3.Is 69521 divisible by 19?
  4. 4.Is 53413 divisible by 10?
  5. 5.Is 23709 divisible by 10?
  6. 6.Is 1369 divisible by 5?
  7. 7.Is 12150 divisible by 5?
  8. 8.Is 132564 divisible by 23?
  9. 9.Is 46333 divisible by 19?
  10. 10.Is 49167 divisible by 9?
  11. 11.Is 56445 divisible by 15?
  12. 12.Is 47580 divisible by 30?
  13. 13.Is 16025 divisible by 4?
  14. 14.Is 54392 divisible by 13?
  15. 15.Is 74587 divisible by 24?
  16. 16.Is 3570 divisible by 5?
  17. 17.Is 9319 divisible by 2?
  18. 18.Is 20768 divisible by 9?
  19. 19.Is 6779 divisible by 5?
  20. 20.Is 12144 divisible by 8?
  21. 21.Is 14591 divisible by 10?
  22. 22.Is 9835 divisible by 7?
  23. 23.Is 13904 divisible by 8?
  24. 24.Is 50761 divisible by 23?
  25. 25.Is 36540 divisible by 30?
  26. 26.Is 33660 divisible by 18?
  27. 27.Is 11743 divisible by 15?
  28. 28.Is 4090 divisible by 8?
  29. 29.Is 48769 divisible by 7?
  30. 30.Is 22662 divisible by 24?
  31. 31.Is 164800 divisible by 24?
  32. 32.Is 114130 divisible by 18?
  33. 33.Is 55927 divisible by 9?
  34. 34.Is 53811 divisible by 9?
  35. 35.Is 11247 divisible by 3?
  36. 36.Is 27448 divisible by 4?
  37. 37.Is 10317 divisible by 2?
  38. 38.Is 3604 divisible by 20?
  39. 39.Is 28663 divisible by 13?
  40. 40.Is 22722 divisible by 11?

Answer key

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

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