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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 277 · 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 21731 divisible by 6?
  2. 2.Is 60605 divisible by 23?
  3. 3.Is 106967 divisible by 20?
  4. 4.Is 44539 divisible by 8?
  5. 5.Is 6244 divisible by 11?
  6. 6.Is 32115 divisible by 30?
  7. 7.Is 140415 divisible by 23?
  8. 8.Is 11442 divisible by 6?
  9. 9.Is 107166 divisible by 18?
  10. 10.Is 87136 divisible by 15?
  11. 11.Is 291 divisible by 4?
  12. 12.Is 82376 divisible by 12?
  13. 13.Is 8821 divisible by 8?
  14. 14.Is 51144 divisible by 15?
  15. 15.Is 8328 divisible by 3?
  16. 16.Is 84672 divisible by 18?
  17. 17.Is 15636 divisible by 24?
  18. 18.Is 3380 divisible by 10?
  19. 19.Is 136272 divisible by 29?
  20. 20.Is 43940 divisible by 7?
  21. 21.Is 1628 divisible by 2?
  22. 22.Is 6229 divisible by 12?
  23. 23.Is 40873 divisible by 13?
  24. 24.Is 26885 divisible by 5?
  25. 25.Is 9205 divisible by 4?
  26. 26.Is 7485 divisible by 3?
  27. 27.Is 20391 divisible by 7?
  28. 28.Is 60000 divisible by 30?
  29. 29.Is 4991 divisible by 2?
  30. 30.Is 57960 divisible by 30?
  31. 31.Is 57485 divisible by 12?
  32. 32.Is 56043 divisible by 13?
  33. 33.Is 11792 divisible by 11?
  34. 34.Is 7622 divisible by 5?
  35. 35.Is 59880 divisible by 10?
  36. 36.Is 16755 divisible by 3?
  37. 37.Is 11565 divisible by 4?
  38. 38.Is 73521 divisible by 18?
  39. 39.Is 13023 divisible by 3?
  40. 40.Is 104940 divisible by 20?

Answer key

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

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