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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 584 · 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 17700 divisible by 6?
  2. 2.Is 19830 divisible by 3?
  3. 3.Is 78424 divisible by 18?
  4. 4.Is 33847 divisible by 11?
  5. 5.Is 50437 divisible by 24?
  6. 6.Is 31001 divisible by 29?
  7. 7.Is 29958 divisible by 24?
  8. 8.Is 70127 divisible by 29?
  9. 9.Is 82044 divisible by 18?
  10. 10.Is 10256 divisible by 8?
  11. 11.Is 70714 divisible by 11?
  12. 12.Is 23106 divisible by 4?
  13. 13.Is 70180 divisible by 11?
  14. 14.Is 17407 divisible by 3?
  15. 15.Is 114244 divisible by 17?
  16. 16.Is 3703 divisible by 24?
  17. 17.Is 39281 divisible by 9?
  18. 18.Is 33398 divisible by 8?
  19. 19.Is 39392 divisible by 8?
  20. 20.Is 3096 divisible by 24?
  21. 21.Is 46382 divisible by 7?
  22. 22.Is 3010 divisible by 5?
  23. 23.Is 106619 divisible by 23?
  24. 24.Is 83 divisible by 5?
  25. 25.Is 16308 divisible by 4?
  26. 26.Is 2447 divisible by 6?
  27. 27.Is 99314 divisible by 23?
  28. 28.Is 1595 divisible by 3?
  29. 29.Is 51256 divisible by 30?
  30. 30.Is 25953 divisible by 12?
  31. 31.Is 3808 divisible by 3?
  32. 32.Is 42340 divisible by 20?
  33. 33.Is 2289 divisible by 12?
  34. 34.Is 98194 divisible by 29?
  35. 35.Is 145211 divisible by 29?
  36. 36.Is 41620 divisible by 10?
  37. 37.Is 16272 divisible by 10?
  38. 38.Is 30038 divisible by 6?
  39. 39.Is 29831 divisible by 6?
  40. 40.Is 973 divisible by 2?

Answer key

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

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