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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 938 · 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 56340 divisible by 11?
  2. 2.Is 14072 divisible by 4?
  3. 3.Is 94704 divisible by 20?
  4. 4.Is 17394 divisible by 13?
  5. 5.Is 3726 divisible by 4?
  6. 6.Is 42674 divisible by 13?
  7. 7.Is 36982 divisible by 15?
  8. 8.Is 20611 divisible by 3?
  9. 9.Is 171622 divisible by 29?
  10. 10.Is 3065 divisible by 4?
  11. 11.Is 21982 divisible by 29?
  12. 12.Is 34979 divisible by 19?
  13. 13.Is 9147 divisible by 2?
  14. 14.Is 63102 divisible by 23?
  15. 15.Is 31120 divisible by 7?
  16. 16.Is 13341 divisible by 2?
  17. 17.Is 6022 divisible by 20?
  18. 18.Is 26652 divisible by 12?
  19. 19.Is 12635 divisible by 6?
  20. 20.Is 456 divisible by 4?
  21. 21.Is 36720 divisible by 15?
  22. 22.Is 11101 divisible by 17?
  23. 23.Is 29355 divisible by 15?
  24. 24.Is 2993 divisible by 13?
  25. 25.Is 76299 divisible by 29?
  26. 26.Is 32647 divisible by 6?
  27. 27.Is 120016 divisible by 18?
  28. 28.Is 1450 divisible by 11?
  29. 29.Is 9096 divisible by 3?
  30. 30.Is 1019 divisible by 6?
  31. 31.Is 5583 divisible by 3?
  32. 32.Is 81 divisible by 2?
  33. 33.Is 25498 divisible by 7?
  34. 34.Is 45612 divisible by 7?
  35. 35.Is 11168 divisible by 10?
  36. 36.Is 42910 divisible by 7?
  37. 37.Is 99876 divisible by 17?
  38. 38.Is 3262 divisible by 2?
  39. 39.Is 28959 divisible by 30?
  40. 40.Is 69694 divisible by 11?

Answer key

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

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