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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 975 · 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 52403 divisible by 13?
  2. 2.Is 107250 divisible by 30?
  3. 3.Is 41032 divisible by 8?
  4. 4.Is 80208 divisible by 24?
  5. 5.Is 131560 divisible by 20?
  6. 6.Is 40553 divisible by 18?
  7. 7.Is 195882 divisible by 30?
  8. 8.Is 166590 divisible by 30?
  9. 9.Is 54723 divisible by 29?
  10. 10.Is 41714 divisible by 15?
  11. 11.Is 26579 divisible by 7?
  12. 12.Is 56995 divisible by 19?
  13. 13.Is 2374 divisible by 2?
  14. 14.Is 18563 divisible by 19?
  15. 15.Is 71106 divisible by 20?
  16. 16.Is 29962 divisible by 5?
  17. 17.Is 14469 divisible by 7?
  18. 18.Is 46812 divisible by 13?
  19. 19.Is 5445 divisible by 3?
  20. 20.Is 12286 divisible by 6?
  21. 21.Is 138740 divisible by 20?
  22. 22.Is 20849 divisible by 13?
  23. 23.Is 10237 divisible by 3?
  24. 24.Is 19372 divisible by 13?
  25. 25.Is 52634 divisible by 9?
  26. 26.Is 7568 divisible by 3?
  27. 27.Is 23143 divisible by 17?
  28. 28.Is 10908 divisible by 2?
  29. 29.Is 4534 divisible by 9?
  30. 30.Is 13086 divisible by 4?
  31. 31.Is 72396 divisible by 15?
  32. 32.Is 36340 divisible by 23?
  33. 33.Is 2991 divisible by 9?
  34. 34.Is 32494 divisible by 11?
  35. 35.Is 21829 divisible by 10?
  36. 36.Is 118333 divisible by 18?
  37. 37.Is 56999 divisible by 20?
  38. 38.Is 27030 divisible by 30?
  39. 39.Is 1027 divisible by 6?
  40. 40.Is 34266 divisible by 10?

Answer key

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

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