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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 775 · 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 99634 divisible by 24?
  2. 2.Is 73560 divisible by 30?
  3. 3.Is 11773 divisible by 4?
  4. 4.Is 5190 divisible by 6?
  5. 5.Is 23345 divisible by 23?
  6. 6.Is 12582 divisible by 18?
  7. 7.Is 23552 divisible by 17?
  8. 8.Is 41751 divisible by 9?
  9. 9.Is 28045 divisible by 10?
  10. 10.Is 15274 divisible by 15?
  11. 11.Is 8127 divisible by 7?
  12. 12.Is 26894 divisible by 4?
  13. 13.Is 15020 divisible by 10?
  14. 14.Is 30372 divisible by 10?
  15. 15.Is 55476 divisible by 20?
  16. 16.Is 7088 divisible by 5?
  17. 17.Is 16463 divisible by 6?
  18. 18.Is 31025 divisible by 5?
  19. 19.Is 17304 divisible by 8?
  20. 20.Is 30033 divisible by 12?
  21. 21.Is 109248 divisible by 24?
  22. 22.Is 70337 divisible by 29?
  23. 23.Is 88317 divisible by 17?
  24. 24.Is 11931 divisible by 3?
  25. 25.Is 17232 divisible by 12?
  26. 26.Is 1725 divisible by 3?
  27. 27.Is 2214 divisible by 9?
  28. 28.Is 66616 divisible by 17?
  29. 29.Is 5720 divisible by 5?
  30. 30.Is 24698 divisible by 5?
  31. 31.Is 2395 divisible by 2?
  32. 32.Is 49936 divisible by 8?
  33. 33.Is 8670 divisible by 4?
  34. 34.Is 5971 divisible by 7?
  35. 35.Is 25560 divisible by 5?
  36. 36.Is 5154 divisible by 2?
  37. 37.Is 50076 divisible by 18?
  38. 38.Is 19588 divisible by 3?
  39. 39.Is 130838 divisible by 19?
  40. 40.Is 540 divisible by 3?

Answer key

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

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