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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 397 · 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 7425 divisible by 30?
  2. 2.Is 3066 divisible by 7?
  3. 3.Is 3787 divisible by 9?
  4. 4.Is 14333 divisible by 10?
  5. 5.Is 18555 divisible by 4?
  6. 6.Is 13578 divisible by 6?
  7. 7.Is 20520 divisible by 30?
  8. 8.Is 22314 divisible by 6?
  9. 9.Is 22152 divisible by 24?
  10. 10.Is 8261 divisible by 12?
  11. 11.Is 1476 divisible by 2?
  12. 12.Is 32052 divisible by 24?
  13. 13.Is 198561 divisible by 30?
  14. 14.Is 29688 divisible by 6?
  15. 15.Is 106122 divisible by 17?
  16. 16.Is 7358 divisible by 4?
  17. 17.Is 14581 divisible by 7?
  18. 18.Is 25060 divisible by 5?
  19. 19.Is 35946 divisible by 6?
  20. 20.Is 68042 divisible by 13?
  21. 21.Is 9951 divisible by 2?
  22. 22.Is 45594 divisible by 18?
  23. 23.Is 28920 divisible by 8?
  24. 24.Is 22142 divisible by 13?
  25. 25.Is 22254 divisible by 4?
  26. 26.Is 39060 divisible by 17?
  27. 27.Is 106172 divisible by 19?
  28. 28.Is 195663 divisible by 29?
  29. 29.Is 29118 divisible by 23?
  30. 30.Is 12420 divisible by 5?
  31. 31.Is 14720 divisible by 10?
  32. 32.Is 8722 divisible by 6?
  33. 33.Is 11010 divisible by 3?
  34. 34.Is 53521 divisible by 10?
  35. 35.Is 47232 divisible by 8?
  36. 36.Is 8941 divisible by 3?
  37. 37.Is 15726 divisible by 5?
  38. 38.Is 9266 divisible by 12?
  39. 39.Is 22167 divisible by 9?
  40. 40.Is 38304 divisible by 24?

Answer key

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

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