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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 716 · 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 1319 divisible by 5?
  2. 2.Is 115776 divisible by 18?
  3. 3.Is 22914 divisible by 19?
  4. 4.Is 17430 divisible by 7?
  5. 5.Is 24848 divisible by 20?
  6. 6.Is 67380 divisible by 30?
  7. 7.Is 22190 divisible by 15?
  8. 8.Is 62019 divisible by 9?
  9. 9.Is 24407 divisible by 17?
  10. 10.Is 59300 divisible by 20?
  11. 11.Is 57891 divisible by 23?
  12. 12.Is 17404 divisible by 5?
  13. 13.Is 112340 divisible by 20?
  14. 14.Is 54865 divisible by 10?
  15. 15.Is 32130 divisible by 17?
  16. 16.Is 34614 divisible by 10?
  17. 17.Is 44001 divisible by 9?
  18. 18.Is 44638 divisible by 11?
  19. 19.Is 7726 divisible by 5?
  20. 20.Is 132573 divisible by 24?
  21. 21.Is 82948 divisible by 12?
  22. 22.Is 56981 divisible by 13?
  23. 23.Is 75394 divisible by 23?
  24. 24.Is 12005 divisible by 6?
  25. 25.Is 662 divisible by 2?
  26. 26.Is 1963 divisible by 2?
  27. 27.Is 7413 divisible by 4?
  28. 28.Is 4089 divisible by 3?
  29. 29.Is 71730 divisible by 30?
  30. 30.Is 42577 divisible by 8?
  31. 31.Is 46943 divisible by 23?
  32. 32.Is 52139 divisible by 19?
  33. 33.Is 130850 divisible by 29?
  34. 34.Is 67760 divisible by 10?
  35. 35.Is 16938 divisible by 9?
  36. 36.Is 54360 divisible by 12?
  37. 37.Is 14854 divisible by 5?
  38. 38.Is 31928 divisible by 8?
  39. 39.Is 68070 divisible by 15?
  40. 40.Is 26186 divisible by 12?

Answer key

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

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