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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 742 · 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 110746 divisible by 29?
  2. 2.Is 120733 divisible by 24?
  3. 3.Is 29219 divisible by 12?
  4. 4.Is 62625 divisible by 10?
  5. 5.Is 5010 divisible by 30?
  6. 6.Is 51348 divisible by 11?
  7. 7.Is 32040 divisible by 8?
  8. 8.Is 6486 divisible by 12?
  9. 9.Is 14663 divisible by 4?
  10. 10.Is 38469 divisible by 9?
  11. 11.Is 31639 divisible by 29?
  12. 12.Is 9682 divisible by 12?
  13. 13.Is 101091 divisible by 19?
  14. 14.Is 27216 divisible by 24?
  15. 15.Is 13341 divisible by 2?
  16. 16.Is 4044 divisible by 2?
  17. 17.Is 23526 divisible by 5?
  18. 18.Is 22854 divisible by 6?
  19. 19.Is 74430 divisible by 15?
  20. 20.Is 36976 divisible by 8?
  21. 21.Is 10650 divisible by 30?
  22. 22.Is 37702 divisible by 10?
  23. 23.Is 50351 divisible by 15?
  24. 24.Is 38084 divisible by 10?
  25. 25.Is 14205 divisible by 15?
  26. 26.Is 61190 divisible by 23?
  27. 27.Is 51621 divisible by 12?
  28. 28.Is 30151 divisible by 20?
  29. 29.Is 88187 divisible by 18?
  30. 30.Is 16620 divisible by 4?
  31. 31.Is 59211 divisible by 9?
  32. 32.Is 51750 divisible by 10?
  33. 33.Is 24353 divisible by 5?
  34. 34.Is 79540 divisible by 20?
  35. 35.Is 167953 divisible by 29?
  36. 36.Is 11041 divisible by 2?
  37. 37.Is 11869 divisible by 13?
  38. 38.Is 12091 divisible by 6?
  39. 39.Is 9570 divisible by 10?
  40. 40.Is 2998 divisible by 2?

Answer key

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

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