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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 500 · 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 13839 divisible by 18?
  2. 2.Is 122634 divisible by 30?
  3. 3.Is 27000 divisible by 8?
  4. 4.Is 148140 divisible by 30?
  5. 5.Is 18174 divisible by 9?
  6. 6.Is 54980 divisible by 20?
  7. 7.Is 14909 divisible by 3?
  8. 8.Is 5013 divisible by 3?
  9. 9.Is 529 divisible by 23?
  10. 10.Is 13800 divisible by 5?
  11. 11.Is 2881 divisible by 3?
  12. 12.Is 27947 divisible by 5?
  13. 13.Is 15873 divisible by 11?
  14. 14.Is 83916 divisible by 12?
  15. 15.Is 21646 divisible by 15?
  16. 16.Is 14787 divisible by 9?
  17. 17.Is 4702 divisible by 2?
  18. 18.Is 75388 divisible by 18?
  19. 19.Is 6310 divisible by 3?
  20. 20.Is 126331 divisible by 19?
  21. 21.Is 23840 divisible by 20?
  22. 22.Is 77373 divisible by 13?
  23. 23.Is 33480 divisible by 30?
  24. 24.Is 13418 divisible by 5?
  25. 25.Is 42583 divisible by 7?
  26. 26.Is 31678 divisible by 15?
  27. 27.Is 4510 divisible by 6?
  28. 28.Is 71859 divisible by 15?
  29. 29.Is 132035 divisible by 20?
  30. 30.Is 1972 divisible by 4?
  31. 31.Is 34177 divisible by 5?
  32. 32.Is 47029 divisible by 7?
  33. 33.Is 5487 divisible by 10?
  34. 34.Is 28127 divisible by 11?
  35. 35.Is 62480 divisible by 11?
  36. 36.Is 1658 divisible by 2?
  37. 37.Is 20453 divisible by 3?
  38. 38.Is 101765 divisible by 18?
  39. 39.Is 24693 divisible by 9?
  40. 40.Is 32085 divisible by 23?

Answer key

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

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