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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 249 · 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 5615 divisible by 2?
  2. 2.Is 31934 divisible by 12?
  3. 3.Is 19714 divisible by 15?
  4. 4.Is 78060 divisible by 12?
  5. 5.Is 52215 divisible by 15?
  6. 6.Is 29209 divisible by 5?
  7. 7.Is 6457 divisible by 11?
  8. 8.Is 16674 divisible by 4?
  9. 9.Is 5496 divisible by 4?
  10. 10.Is 194370 divisible by 30?
  11. 11.Is 23160 divisible by 4?
  12. 12.Is 49572 divisible by 19?
  13. 13.Is 108467 divisible by 24?
  14. 14.Is 14045 divisible by 4?
  15. 15.Is 11853 divisible by 4?
  16. 16.Is 90493 divisible by 19?
  17. 17.Is 18792 divisible by 19?
  18. 18.Is 993 divisible by 11?
  19. 19.Is 14920 divisible by 8?
  20. 20.Is 38232 divisible by 9?
  21. 21.Is 3191 divisible by 9?
  22. 22.Is 113543 divisible by 23?
  23. 23.Is 31027 divisible by 19?
  24. 24.Is 29060 divisible by 29?
  25. 25.Is 32475 divisible by 15?
  26. 26.Is 161472 divisible by 29?
  27. 27.Is 60063 divisible by 15?
  28. 28.Is 136703 divisible by 23?
  29. 29.Is 15821 divisible by 23?
  30. 30.Is 64650 divisible by 15?
  31. 31.Is 1387 divisible by 6?
  32. 32.Is 14542 divisible by 11?
  33. 33.Is 62942 divisible by 12?
  34. 34.Is 28900 divisible by 5?
  35. 35.Is 89672 divisible by 17?
  36. 36.Is 42456 divisible by 29?
  37. 37.Is 3547 divisible by 6?
  38. 38.Is 44244 divisible by 18?
  39. 39.Is 25509 divisible by 5?
  40. 40.Is 5566 divisible by 7?

Answer key

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

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