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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 849 · 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 57471 divisible by 15?
  2. 2.Is 18280 divisible by 5?
  3. 3.Is 137360 divisible by 20?
  4. 4.Is 4696 divisible by 4?
  5. 5.Is 133020 divisible by 20?
  6. 6.Is 17763 divisible by 7?
  7. 7.Is 29024 divisible by 5?
  8. 8.Is 87713 divisible by 17?
  9. 9.Is 21972 divisible by 8?
  10. 10.Is 74960 divisible by 23?
  11. 11.Is 79410 divisible by 30?
  12. 12.Is 34952 divisible by 8?
  13. 13.Is 3344 divisible by 8?
  14. 14.Is 26240 divisible by 10?
  15. 15.Is 20042 divisible by 7?
  16. 16.Is 558 divisible by 18?
  17. 17.Is 20752 divisible by 4?
  18. 18.Is 121996 divisible by 30?
  19. 19.Is 18126 divisible by 5?
  20. 20.Is 17172 divisible by 12?
  21. 21.Is 61737 divisible by 17?
  22. 22.Is 92017 divisible by 19?
  23. 23.Is 49908 divisible by 23?
  24. 24.Is 540 divisible by 18?
  25. 25.Is 51840 divisible by 20?
  26. 26.Is 12644 divisible by 4?
  27. 27.Is 141312 divisible by 29?
  28. 28.Is 13286 divisible by 2?
  29. 29.Is 19572 divisible by 4?
  30. 30.Is 93570 divisible by 15?
  31. 31.Is 129352 divisible by 19?
  32. 32.Is 9451 divisible by 13?
  33. 33.Is 13272 divisible by 11?
  34. 34.Is 5413 divisible by 7?
  35. 35.Is 5807 divisible by 2?
  36. 36.Is 46130 divisible by 17?
  37. 37.Is 8048 divisible by 2?
  38. 38.Is 47285 divisible by 7?
  39. 39.Is 2383 divisible by 19?
  40. 40.Is 65726 divisible by 30?

Answer key

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

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