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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 22 · 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 26798 divisible by 12?
  2. 2.Is 186065 divisible by 29?
  3. 3.Is 36975 divisible by 15?
  4. 4.Is 48331 divisible by 30?
  5. 5.Is 25856 divisible by 4?
  6. 6.Is 6860 divisible by 8?
  7. 7.Is 2340 divisible by 19?
  8. 8.Is 20428 divisible by 3?
  9. 9.Is 11598 divisible by 6?
  10. 10.Is 4421 divisible by 7?
  11. 11.Is 60480 divisible by 20?
  12. 12.Is 20306 divisible by 4?
  13. 13.Is 7533 divisible by 2?
  14. 14.Is 38925 divisible by 9?
  15. 15.Is 114215 divisible by 18?
  16. 16.Is 40867 divisible by 7?
  17. 17.Is 27092 divisible by 4?
  18. 18.Is 67820 divisible by 20?
  19. 19.Is 10642 divisible by 4?
  20. 20.Is 84773 divisible by 13?
  21. 21.Is 88830 divisible by 18?
  22. 22.Is 75568 divisible by 11?
  23. 23.Is 16087 divisible by 30?
  24. 24.Is 544 divisible by 17?
  25. 25.Is 4949 divisible by 5?
  26. 26.Is 95243 divisible by 23?
  27. 27.Is 36787 divisible by 6?
  28. 28.Is 41285 divisible by 6?
  29. 29.Is 29645 divisible by 5?
  30. 30.Is 11025 divisible by 9?
  31. 31.Is 73697 divisible by 13?
  32. 32.Is 31241 divisible by 10?
  33. 33.Is 8859 divisible by 2?
  34. 34.Is 49912 divisible by 17?
  35. 35.Is 20544 divisible by 30?
  36. 36.Is 22391 divisible by 5?
  37. 37.Is 12365 divisible by 6?
  38. 38.Is 15182 divisible by 18?
  39. 39.Is 1523 divisible by 3?
  40. 40.Is 143309 divisible by 30?

Answer key

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

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