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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 983 · 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 17128 divisible by 15?
  2. 2.Is 15457 divisible by 10?
  3. 3.Is 13120 divisible by 5?
  4. 4.Is 10350 divisible by 23?
  5. 5.Is 88827 divisible by 29?
  6. 6.Is 6696 divisible by 2?
  7. 7.Is 6564 divisible by 9?
  8. 8.Is 65405 divisible by 15?
  9. 9.Is 89056 divisible by 23?
  10. 10.Is 52992 divisible by 19?
  11. 11.Is 111621 divisible by 29?
  12. 12.Is 4332 divisible by 2?
  13. 13.Is 25905 divisible by 12?
  14. 14.Is 12514 divisible by 30?
  15. 15.Is 77533 divisible by 13?
  16. 16.Is 99902 divisible by 19?
  17. 17.Is 118099 divisible by 17?
  18. 18.Is 318 divisible by 5?
  19. 19.Is 59192 divisible by 11?
  20. 20.Is 101304 divisible by 18?
  21. 21.Is 4106 divisible by 2?
  22. 22.Is 23796 divisible by 6?
  23. 23.Is 1073 divisible by 2?
  24. 24.Is 22540 divisible by 4?
  25. 25.Is 16628 divisible by 4?
  26. 26.Is 50256 divisible by 10?
  27. 27.Is 12547 divisible by 5?
  28. 28.Is 92278 divisible by 29?
  29. 29.Is 137876 divisible by 20?
  30. 30.Is 20478 divisible by 7?
  31. 31.Is 21696 divisible by 6?
  32. 32.Is 7881 divisible by 6?
  33. 33.Is 15043 divisible by 9?
  34. 34.Is 56250 divisible by 11?
  35. 35.Is 50743 divisible by 10?
  36. 36.Is 80115 divisible by 15?
  37. 37.Is 4489 divisible by 24?
  38. 38.Is 67820 divisible by 10?
  39. 39.Is 72726 divisible by 17?
  40. 40.Is 206220 divisible by 30?

Answer key

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

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