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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 316 · 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 34092 divisible by 6?
  2. 2.Is 11697 divisible by 3?
  3. 3.Is 18481 divisible by 3?
  4. 4.Is 131214 divisible by 19?
  5. 5.Is 3432 divisible by 6?
  6. 6.Is 26769 divisible by 5?
  7. 7.Is 118233 divisible by 18?
  8. 8.Is 25388 divisible by 19?
  9. 9.Is 56763 divisible by 9?
  10. 10.Is 30504 divisible by 12?
  11. 11.Is 14499 divisible by 6?
  12. 12.Is 20290 divisible by 6?
  13. 13.Is 80019 divisible by 17?
  14. 14.Is 30078 divisible by 6?
  15. 15.Is 20571 divisible by 3?
  16. 16.Is 121279 divisible by 23?
  17. 17.Is 60412 divisible by 9?
  18. 18.Is 565 divisible by 2?
  19. 19.Is 16962 divisible by 3?
  20. 20.Is 187440 divisible by 30?
  21. 21.Is 17678 divisible by 9?
  22. 22.Is 33748 divisible by 11?
  23. 23.Is 33580 divisible by 6?
  24. 24.Is 13271 divisible by 20?
  25. 25.Is 53161 divisible by 9?
  26. 26.Is 39537 divisible by 11?
  27. 27.Is 46940 divisible by 24?
  28. 28.Is 9036 divisible by 12?
  29. 29.Is 47608 divisible by 8?
  30. 30.Is 48140 divisible by 20?
  31. 31.Is 38467 divisible by 13?
  32. 32.Is 22536 divisible by 8?
  33. 33.Is 1949 divisible by 2?
  34. 34.Is 18978 divisible by 7?
  35. 35.Is 8701 divisible by 15?
  36. 36.Is 66540 divisible by 10?
  37. 37.Is 35710 divisible by 10?
  38. 38.Is 18523 divisible by 23?
  39. 39.Is 61239 divisible by 10?
  40. 40.Is 24282 divisible by 18?

Answer key

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

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