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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 442 · 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 1918 divisible by 7?
  2. 2.Is 36652 divisible by 17?
  3. 3.Is 11638 divisible by 4?
  4. 4.Is 26688 divisible by 6?
  5. 5.Is 1384 divisible by 2?
  6. 6.Is 100320 divisible by 19?
  7. 7.Is 119430 divisible by 30?
  8. 8.Is 48300 divisible by 9?
  9. 9.Is 14268 divisible by 4?
  10. 10.Is 22435 divisible by 9?
  11. 11.Is 6292 divisible by 24?
  12. 12.Is 22304 divisible by 4?
  13. 13.Is 46001 divisible by 11?
  14. 14.Is 26661 divisible by 13?
  15. 15.Is 22883 divisible by 10?
  16. 16.Is 18499 divisible by 13?
  17. 17.Is 24787 divisible by 5?
  18. 18.Is 131026 divisible by 19?
  19. 19.Is 43636 divisible by 19?
  20. 20.Is 6311 divisible by 9?
  21. 21.Is 23256 divisible by 18?
  22. 22.Is 75307 divisible by 13?
  23. 23.Is 117120 divisible by 24?
  24. 24.Is 57 divisible by 3?
  25. 25.Is 70431 divisible by 17?
  26. 26.Is 24558 divisible by 6?
  27. 27.Is 110190 divisible by 20?
  28. 28.Is 77952 divisible by 29?
  29. 29.Is 81432 divisible by 13?
  30. 30.Is 76950 divisible by 18?
  31. 31.Is 31102 divisible by 5?
  32. 32.Is 20420 divisible by 3?
  33. 33.Is 6386 divisible by 3?
  34. 34.Is 34676 divisible by 5?
  35. 35.Is 14149 divisible by 15?
  36. 36.Is 190182 divisible by 29?
  37. 37.Is 8838 divisible by 4?
  38. 38.Is 110646 divisible by 18?
  39. 39.Is 6340 divisible by 4?
  40. 40.Is 47215 divisible by 7?

Answer key

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

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