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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 303 · 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 18115 divisible by 24?
  2. 2.Is 1224 divisible by 10?
  3. 3.Is 98724 divisible by 17?
  4. 4.Is 106964 divisible by 17?
  5. 5.Is 90026 divisible by 20?
  6. 6.Is 181917 divisible by 29?
  7. 7.Is 16546 divisible by 8?
  8. 8.Is 192705 divisible by 29?
  9. 9.Is 16525 divisible by 7?
  10. 10.Is 52419 divisible by 8?
  11. 11.Is 137245 divisible by 20?
  12. 12.Is 50868 divisible by 29?
  13. 13.Is 971 divisible by 5?
  14. 14.Is 8926 divisible by 3?
  15. 15.Is 958 divisible by 2?
  16. 16.Is 152292 divisible by 23?
  17. 17.Is 30958 divisible by 5?
  18. 18.Is 44406 divisible by 9?
  19. 19.Is 633 divisible by 6?
  20. 20.Is 41210 divisible by 12?
  21. 21.Is 157309 divisible by 23?
  22. 22.Is 12922 divisible by 2?
  23. 23.Is 7535 divisible by 2?
  24. 24.Is 10965 divisible by 17?
  25. 25.Is 17328 divisible by 12?
  26. 26.Is 6560 divisible by 8?
  27. 27.Is 20080 divisible by 15?
  28. 28.Is 15456 divisible by 7?
  29. 29.Is 7787 divisible by 10?
  30. 30.Is 8218 divisible by 7?
  31. 31.Is 131215 divisible by 19?
  32. 32.Is 43509 divisible by 7?
  33. 33.Is 26467 divisible by 11?
  34. 34.Is 6477 divisible by 10?
  35. 35.Is 46105 divisible by 10?
  36. 36.Is 17685 divisible by 3?
  37. 37.Is 36670 divisible by 19?
  38. 38.Is 33650 divisible by 5?
  39. 39.Is 22686 divisible by 4?
  40. 40.Is 850 divisible by 10?

Answer key

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

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