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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 701 · 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 25596 divisible by 7?
  2. 2.Is 10425 divisible by 20?
  3. 3.Is 4978 divisible by 12?
  4. 4.Is 19017 divisible by 4?
  5. 5.Is 16786 divisible by 9?
  6. 6.Is 22154 divisible by 19?
  7. 7.Is 75571 divisible by 19?
  8. 8.Is 9109 divisible by 24?
  9. 9.Is 763 divisible by 2?
  10. 10.Is 36076 divisible by 29?
  11. 11.Is 10168 divisible by 8?
  12. 12.Is 174870 divisible by 29?
  13. 13.Is 36257 divisible by 7?
  14. 14.Is 206550 divisible by 30?
  15. 15.Is 20501 divisible by 4?
  16. 16.Is 42371 divisible by 7?
  17. 17.Is 117405 divisible by 23?
  18. 18.Is 95703 divisible by 23?
  19. 19.Is 12530 divisible by 7?
  20. 20.Is 3269 divisible by 3?
  21. 21.Is 111549 divisible by 19?
  22. 22.Is 18634 divisible by 9?
  23. 23.Is 44750 divisible by 10?
  24. 24.Is 103139 divisible by 15?
  25. 25.Is 5868 divisible by 9?
  26. 26.Is 207060 divisible by 30?
  27. 27.Is 42324 divisible by 7?
  28. 28.Is 32680 divisible by 5?
  29. 29.Is 26305 divisible by 5?
  30. 30.Is 3282 divisible by 12?
  31. 31.Is 17875 divisible by 23?
  32. 32.Is 49628 divisible by 11?
  33. 33.Is 75086 divisible by 19?
  34. 34.Is 64272 divisible by 24?
  35. 35.Is 20002 divisible by 4?
  36. 36.Is 107445 divisible by 29?
  37. 37.Is 31533 divisible by 23?
  38. 38.Is 48005 divisible by 8?
  39. 39.Is 18462 divisible by 4?
  40. 40.Is 30690 divisible by 30?

Answer key

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

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