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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 879 · 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 59714 divisible by 20?
  2. 2.Is 135945 divisible by 23?
  3. 3.Is 13667 divisible by 5?
  4. 4.Is 20539 divisible by 10?
  5. 5.Is 22000 divisible by 17?
  6. 6.Is 8676 divisible by 9?
  7. 7.Is 42541 divisible by 19?
  8. 8.Is 54450 divisible by 18?
  9. 9.Is 139308 divisible by 20?
  10. 10.Is 75827 divisible by 24?
  11. 11.Is 47215 divisible by 19?
  12. 12.Is 36363 divisible by 18?
  13. 13.Is 75718 divisible by 13?
  14. 14.Is 24661 divisible by 7?
  15. 15.Is 79495 divisible by 13?
  16. 16.Is 14350 divisible by 15?
  17. 17.Is 23969 divisible by 13?
  18. 18.Is 31409 divisible by 7?
  19. 19.Is 105630 divisible by 30?
  20. 20.Is 55500 divisible by 12?
  21. 21.Is 13643 divisible by 10?
  22. 22.Is 57697 divisible by 12?
  23. 23.Is 62910 divisible by 15?
  24. 24.Is 26487 divisible by 7?
  25. 25.Is 17439 divisible by 3?
  26. 26.Is 10620 divisible by 4?
  27. 27.Is 4108 divisible by 6?
  28. 28.Is 12125 divisible by 2?
  29. 29.Is 27521 divisible by 4?
  30. 30.Is 41247 divisible by 12?
  31. 31.Is 125658 divisible by 18?
  32. 32.Is 18594 divisible by 8?
  33. 33.Is 13692 divisible by 7?
  34. 34.Is 15220 divisible by 4?
  35. 35.Is 43835 divisible by 20?
  36. 36.Is 61393 divisible by 15?
  37. 37.Is 20438 divisible by 3?
  38. 38.Is 54201 divisible by 12?
  39. 39.Is 96304 divisible by 29?
  40. 40.Is 1352 divisible by 8?

Answer key

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

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