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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 678 · 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 29865 divisible by 5?
  2. 2.Is 19113 divisible by 4?
  3. 3.Is 35176 divisible by 24?
  4. 4.Is 25170 divisible by 6?
  5. 5.Is 24380 divisible by 20?
  6. 6.Is 43244 divisible by 13?
  7. 7.Is 2442 divisible by 2?
  8. 8.Is 63580 divisible by 10?
  9. 9.Is 31707 divisible by 20?
  10. 10.Is 8761 divisible by 2?
  11. 11.Is 109770 divisible by 30?
  12. 12.Is 26962 divisible by 6?
  13. 13.Is 58124 divisible by 10?
  14. 14.Is 14220 divisible by 10?
  15. 15.Is 16480 divisible by 5?
  16. 16.Is 6055 divisible by 4?
  17. 17.Is 39891 divisible by 10?
  18. 18.Is 68799 divisible by 13?
  19. 19.Is 202110 divisible by 30?
  20. 20.Is 21784 divisible by 5?
  21. 21.Is 17898 divisible by 19?
  22. 22.Is 19637 divisible by 5?
  23. 23.Is 22082 divisible by 4?
  24. 24.Is 7695 divisible by 9?
  25. 25.Is 48893 divisible by 13?
  26. 26.Is 108537 divisible by 19?
  27. 27.Is 10535 divisible by 3?
  28. 28.Is 45680 divisible by 20?
  29. 29.Is 18384 divisible by 23?
  30. 30.Is 17144 divisible by 4?
  31. 31.Is 27602 divisible by 20?
  32. 32.Is 22425 divisible by 13?
  33. 33.Is 190560 divisible by 30?
  34. 34.Is 31908 divisible by 6?
  35. 35.Is 18468 divisible by 9?
  36. 36.Is 54685 divisible by 11?
  37. 37.Is 45306 divisible by 18?
  38. 38.Is 16530 divisible by 7?
  39. 39.Is 12817 divisible by 5?
  40. 40.Is 41655 divisible by 11?

Answer key

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

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