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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 839 · 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 120202 divisible by 29?
  2. 2.Is 25833 divisible by 10?
  3. 3.Is 2432 divisible by 4?
  4. 4.Is 130770 divisible by 30?
  5. 5.Is 198231 divisible by 29?
  6. 6.Is 1394 divisible by 30?
  7. 7.Is 25167 divisible by 8?
  8. 8.Is 205199 divisible by 30?
  9. 9.Is 119736 divisible by 24?
  10. 10.Is 74114 divisible by 17?
  11. 11.Is 115931 divisible by 20?
  12. 12.Is 41073 divisible by 20?
  13. 13.Is 2176 divisible by 4?
  14. 14.Is 17811 divisible by 9?
  15. 15.Is 12589 divisible by 30?
  16. 16.Is 37194 divisible by 9?
  17. 17.Is 77232 divisible by 24?
  18. 18.Is 7950 divisible by 15?
  19. 19.Is 30528 divisible by 6?
  20. 20.Is 29277 divisible by 29?
  21. 21.Is 30267 divisible by 9?
  22. 22.Is 89827 divisible by 29?
  23. 23.Is 6060 divisible by 12?
  24. 24.Is 127897 divisible by 30?
  25. 25.Is 81630 divisible by 30?
  26. 26.Is 42945 divisible by 7?
  27. 27.Is 12916 divisible by 2?
  28. 28.Is 21337 divisible by 5?
  29. 29.Is 26808 divisible by 6?
  30. 30.Is 4367 divisible by 2?
  31. 31.Is 121190 divisible by 29?
  32. 32.Is 64614 divisible by 11?
  33. 33.Is 3050 divisible by 5?
  34. 34.Is 21520 divisible by 20?
  35. 35.Is 71478 divisible by 11?
  36. 36.Is 45307 divisible by 24?
  37. 37.Is 35244 divisible by 9?
  38. 38.Is 60588 divisible by 9?
  39. 39.Is 19391 divisible by 5?
  40. 40.Is 73297 divisible by 13?

Answer key

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

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