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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 715 · 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 17715 divisible by 8?
  2. 2.Is 62345 divisible by 9?
  3. 3.Is 10656 divisible by 4?
  4. 4.Is 15183 divisible by 9?
  5. 5.Is 35715 divisible by 15?
  6. 6.Is 33390 divisible by 18?
  7. 7.Is 51491 divisible by 11?
  8. 8.Is 23789 divisible by 24?
  9. 9.Is 45118 divisible by 17?
  10. 10.Is 131760 divisible by 30?
  11. 11.Is 25553 divisible by 9?
  12. 12.Is 81825 divisible by 18?
  13. 13.Is 5254 divisible by 2?
  14. 14.Is 14816 divisible by 30?
  15. 15.Is 7828 divisible by 4?
  16. 16.Is 52380 divisible by 9?
  17. 17.Is 164943 divisible by 30?
  18. 18.Is 76705 divisible by 23?
  19. 19.Is 87894 divisible by 13?
  20. 20.Is 33930 divisible by 9?
  21. 21.Is 107184 divisible by 29?
  22. 22.Is 5610 divisible by 20?
  23. 23.Is 47152 divisible by 7?
  24. 24.Is 29965 divisible by 9?
  25. 25.Is 7130 divisible by 18?
  26. 26.Is 19972 divisible by 15?
  27. 27.Is 197130 divisible by 29?
  28. 28.Is 877 divisible by 4?
  29. 29.Is 59668 divisible by 18?
  30. 30.Is 46064 divisible by 30?
  31. 31.Is 18642 divisible by 6?
  32. 32.Is 1605 divisible by 4?
  33. 33.Is 57640 divisible by 11?
  34. 34.Is 15694 divisible by 19?
  35. 35.Is 1971 divisible by 7?
  36. 36.Is 118135 divisible by 18?
  37. 37.Is 46128 divisible by 8?
  38. 38.Is 40509 divisible by 7?
  39. 39.Is 121353 divisible by 18?
  40. 40.Is 94651 divisible by 15?

Answer key

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

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