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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 767 · 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 151807 divisible by 24?
  2. 2.Is 5958 divisible by 7?
  3. 3.Is 26580 divisible by 6?
  4. 4.Is 110064 divisible by 24?
  5. 5.Is 69221 divisible by 23?
  6. 6.Is 24840 divisible by 18?
  7. 7.Is 135560 divisible by 20?
  8. 8.Is 17073 divisible by 17?
  9. 9.Is 58374 divisible by 9?
  10. 10.Is 3210 divisible by 15?
  11. 11.Is 33891 divisible by 6?
  12. 12.Is 975 divisible by 15?
  13. 13.Is 2900 divisible by 20?
  14. 14.Is 29901 divisible by 6?
  15. 15.Is 80674 divisible by 19?
  16. 16.Is 52170 divisible by 30?
  17. 17.Is 37710 divisible by 6?
  18. 18.Is 4964 divisible by 6?
  19. 19.Is 66420 divisible by 15?
  20. 20.Is 43108 divisible by 13?
  21. 21.Is 56507 divisible by 18?
  22. 22.Is 25949 divisible by 8?
  23. 23.Is 41087 divisible by 7?
  24. 24.Is 53471 divisible by 29?
  25. 25.Is 56355 divisible by 13?
  26. 26.Is 6850 divisible by 18?
  27. 27.Is 161327 divisible by 29?
  28. 28.Is 647 divisible by 30?
  29. 29.Is 46017 divisible by 7?
  30. 30.Is 23528 divisible by 17?
  31. 31.Is 62974 divisible by 18?
  32. 32.Is 7175 divisible by 10?
  33. 33.Is 91596 divisible by 30?
  34. 34.Is 57600 divisible by 18?
  35. 35.Is 99918 divisible by 18?
  36. 36.Is 116575 divisible by 18?
  37. 37.Is 27979 divisible by 7?
  38. 38.Is 11575 divisible by 2?
  39. 39.Is 24900 divisible by 15?
  40. 40.Is 22680 divisible by 9?

Answer key

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

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