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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 934 · 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 26431 divisible by 13?
  2. 2.Is 39725 divisible by 30?
  3. 3.Is 16360 divisible by 4?
  4. 4.Is 31075 divisible by 5?
  5. 5.Is 59668 divisible by 19?
  6. 6.Is 108756 divisible by 19?
  7. 7.Is 164647 divisible by 30?
  8. 8.Is 5520 divisible by 23?
  9. 9.Is 48315 divisible by 8?
  10. 10.Is 167008 divisible by 24?
  11. 11.Is 15462 divisible by 6?
  12. 12.Is 77295 divisible by 13?
  13. 13.Is 55796 divisible by 29?
  14. 14.Is 6475 divisible by 19?
  15. 15.Is 2069 divisible by 3?
  16. 16.Is 24489 divisible by 15?
  17. 17.Is 2670 divisible by 2?
  18. 18.Is 13201 divisible by 4?
  19. 19.Is 50512 divisible by 8?
  20. 20.Is 7926 divisible by 8?
  21. 21.Is 14440 divisible by 4?
  22. 22.Is 96519 divisible by 29?
  23. 23.Is 5095 divisible by 5?
  24. 24.Is 8250 divisible by 11?
  25. 25.Is 20296 divisible by 4?
  26. 26.Is 9624 divisible by 12?
  27. 27.Is 11576 divisible by 7?
  28. 28.Is 169230 divisible by 30?
  29. 29.Is 7189 divisible by 7?
  30. 30.Is 112159 divisible by 19?
  31. 31.Is 25992 divisible by 18?
  32. 32.Is 27385 divisible by 4?
  33. 33.Is 58107 divisible by 24?
  34. 34.Is 9999 divisible by 11?
  35. 35.Is 93058 divisible by 23?
  36. 36.Is 56401 divisible by 20?
  37. 37.Is 35852 divisible by 7?
  38. 38.Is 17402 divisible by 11?
  39. 39.Is 56160 divisible by 30?
  40. 40.Is 20530 divisible by 3?

Answer key

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

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