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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 910 · 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 44091 divisible by 23?
  2. 2.Is 83422 divisible by 29?
  3. 3.Is 110111 divisible by 18?
  4. 4.Is 81357 divisible by 19?
  5. 5.Is 35826 divisible by 7?
  6. 6.Is 10022 divisible by 10?
  7. 7.Is 108381 divisible by 20?
  8. 8.Is 65940 divisible by 12?
  9. 9.Is 21345 divisible by 5?
  10. 10.Is 46590 divisible by 15?
  11. 11.Is 30065 divisible by 12?
  12. 12.Is 50253 divisible by 9?
  13. 13.Is 37367 divisible by 10?
  14. 14.Is 79470 divisible by 15?
  15. 15.Is 106799 divisible by 19?
  16. 16.Is 27415 divisible by 4?
  17. 17.Is 44298 divisible by 9?
  18. 18.Is 193662 divisible by 29?
  19. 19.Is 44366 divisible by 7?
  20. 20.Is 62815 divisible by 19?
  21. 21.Is 20631 divisible by 13?
  22. 22.Is 114323 divisible by 19?
  23. 23.Is 113679 divisible by 17?
  24. 24.Is 5261 divisible by 4?
  25. 25.Is 8569 divisible by 2?
  26. 26.Is 53394 divisible by 11?
  27. 27.Is 12156 divisible by 12?
  28. 28.Is 55380 divisible by 13?
  29. 29.Is 7774 divisible by 2?
  30. 30.Is 10275 divisible by 4?
  31. 31.Is 10823 divisible by 6?
  32. 32.Is 12084 divisible by 12?
  33. 33.Is 19258 divisible by 8?
  34. 34.Is 17680 divisible by 8?
  35. 35.Is 48972 divisible by 7?
  36. 36.Is 8570 divisible by 13?
  37. 37.Is 10479 divisible by 2?
  38. 38.Is 21438 divisible by 9?
  39. 39.Is 5614 divisible by 2?
  40. 40.Is 125680 divisible by 20?

Answer key

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

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