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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 309 · 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 14215 divisible by 4?
  2. 2.Is 11614 divisible by 7?
  3. 3.Is 34438 divisible by 10?
  4. 4.Is 13992 divisible by 6?
  5. 5.Is 28499 divisible by 18?
  6. 6.Is 32147 divisible by 12?
  7. 7.Is 13157 divisible by 5?
  8. 8.Is 110093 divisible by 17?
  9. 9.Is 34848 divisible by 6?
  10. 10.Is 89751 divisible by 13?
  11. 11.Is 15369 divisible by 3?
  12. 12.Is 8852 divisible by 2?
  13. 13.Is 72542 divisible by 13?
  14. 14.Is 1848 divisible by 4?
  15. 15.Is 786 divisible by 2?
  16. 16.Is 11052 divisible by 2?
  17. 17.Is 56688 divisible by 13?
  18. 18.Is 38240 divisible by 20?
  19. 19.Is 39179 divisible by 7?
  20. 20.Is 53472 divisible by 12?
  21. 21.Is 27211 divisible by 18?
  22. 22.Is 52868 divisible by 9?
  23. 23.Is 2564 divisible by 3?
  24. 24.Is 11240 divisible by 20?
  25. 25.Is 55568 divisible by 23?
  26. 26.Is 96748 divisible by 19?
  27. 27.Is 97579 divisible by 19?
  28. 28.Is 6680 divisible by 8?
  29. 29.Is 44558 divisible by 24?
  30. 30.Is 54660 divisible by 9?
  31. 31.Is 46598 divisible by 23?
  32. 32.Is 24489 divisible by 12?
  33. 33.Is 56550 divisible by 15?
  34. 34.Is 108964 divisible by 18?
  35. 35.Is 119761 divisible by 23?
  36. 36.Is 40723 divisible by 6?
  37. 37.Is 4820 divisible by 10?
  38. 38.Is 45983 divisible by 7?
  39. 39.Is 65139 divisible by 23?
  40. 40.Is 73440 divisible by 30?

Answer key

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

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