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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 61 · 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 193894 divisible by 29?
  2. 2.Is 11092 divisible by 2?
  3. 3.Is 44897 divisible by 7?
  4. 4.Is 9800 divisible by 20?
  5. 5.Is 9774 divisible by 2?
  6. 6.Is 23480 divisible by 6?
  7. 7.Is 59740 divisible by 29?
  8. 8.Is 103008 divisible by 29?
  9. 9.Is 15749 divisible by 11?
  10. 10.Is 184800 divisible by 30?
  11. 11.Is 73775 divisible by 30?
  12. 12.Is 57288 divisible by 24?
  13. 13.Is 20521 divisible by 13?
  14. 14.Is 1512 divisible by 7?
  15. 15.Is 53868 divisible by 17?
  16. 16.Is 119567 divisible by 19?
  17. 17.Is 4410 divisible by 3?
  18. 18.Is 3468 divisible by 4?
  19. 19.Is 22250 divisible by 5?
  20. 20.Is 37128 divisible by 24?
  21. 21.Is 61440 divisible by 9?
  22. 22.Is 6692 divisible by 7?
  23. 23.Is 1711 divisible by 3?
  24. 24.Is 96465 divisible by 15?
  25. 25.Is 32424 divisible by 24?
  26. 26.Is 14151 divisible by 10?
  27. 27.Is 53671 divisible by 24?
  28. 28.Is 12060 divisible by 18?
  29. 29.Is 183636 divisible by 30?
  30. 30.Is 94947 divisible by 19?
  31. 31.Is 16758 divisible by 7?
  32. 32.Is 26109 divisible by 9?
  33. 33.Is 74797 divisible by 18?
  34. 34.Is 27492 divisible by 4?
  35. 35.Is 42871 divisible by 17?
  36. 36.Is 4609 divisible by 2?
  37. 37.Is 37146 divisible by 30?
  38. 38.Is 17930 divisible by 11?
  39. 39.Is 46306 divisible by 13?
  40. 40.Is 31543 divisible by 7?

Answer key

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

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