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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 698 · 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 17392 divisible by 20?
  2. 2.Is 13133 divisible by 23?
  3. 3.Is 10764 divisible by 18?
  4. 4.Is 1462 divisible by 17?
  5. 5.Is 29488 divisible by 19?
  6. 6.Is 61798 divisible by 11?
  7. 7.Is 159183 divisible by 23?
  8. 8.Is 2943 divisible by 2?
  9. 9.Is 61239 divisible by 13?
  10. 10.Is 9514 divisible by 8?
  11. 11.Is 39492 divisible by 12?
  12. 12.Is 33504 divisible by 6?
  13. 13.Is 23636 divisible by 17?
  14. 14.Is 10620 divisible by 5?
  15. 15.Is 28248 divisible by 9?
  16. 16.Is 15216 divisible by 15?
  17. 17.Is 39324 divisible by 8?
  18. 18.Is 17612 divisible by 17?
  19. 19.Is 77215 divisible by 15?
  20. 20.Is 18893 divisible by 17?
  21. 21.Is 45389 divisible by 7?
  22. 22.Is 145058 divisible by 29?
  23. 23.Is 2177 divisible by 2?
  24. 24.Is 33777 divisible by 20?
  25. 25.Is 8512 divisible by 4?
  26. 26.Is 98940 divisible by 30?
  27. 27.Is 13823 divisible by 5?
  28. 28.Is 15283 divisible by 29?
  29. 29.Is 42435 divisible by 17?
  30. 30.Is 47796 divisible by 7?
  31. 31.Is 7985 divisible by 8?
  32. 32.Is 225 divisible by 15?
  33. 33.Is 40817 divisible by 17?
  34. 34.Is 38421 divisible by 9?
  35. 35.Is 12378 divisible by 3?
  36. 36.Is 10048 divisible by 8?
  37. 37.Is 31861 divisible by 12?
  38. 38.Is 53468 divisible by 9?
  39. 39.Is 1519 divisible by 8?
  40. 40.Is 19408 divisible by 4?

Answer key

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

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