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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 300 · 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 22023 divisible by 4?
  2. 2.Is 70524 divisible by 24?
  3. 3.Is 42672 divisible by 24?
  4. 4.Is 10902 divisible by 23?
  5. 5.Is 18676 divisible by 29?
  6. 6.Is 1378 divisible by 3?
  7. 7.Is 17578 divisible by 11?
  8. 8.Is 97065 divisible by 15?
  9. 9.Is 836 divisible by 2?
  10. 10.Is 5182 divisible by 4?
  11. 11.Is 29496 divisible by 8?
  12. 12.Is 53328 divisible by 24?
  13. 13.Is 29430 divisible by 5?
  14. 14.Is 7670 divisible by 3?
  15. 15.Is 30287 divisible by 17?
  16. 16.Is 11811 divisible by 7?
  17. 17.Is 14706 divisible by 19?
  18. 18.Is 12834 divisible by 29?
  19. 19.Is 68254 divisible by 13?
  20. 20.Is 29108 divisible by 19?
  21. 21.Is 41905 divisible by 9?
  22. 22.Is 4813 divisible by 2?
  23. 23.Is 26350 divisible by 10?
  24. 24.Is 43872 divisible by 9?
  25. 25.Is 57133 divisible by 9?
  26. 26.Is 57726 divisible by 19?
  27. 27.Is 21943 divisible by 18?
  28. 28.Is 8185 divisible by 5?
  29. 29.Is 48464 divisible by 8?
  30. 30.Is 4572 divisible by 9?
  31. 31.Is 12659 divisible by 8?
  32. 32.Is 3842 divisible by 9?
  33. 33.Is 99441 divisible by 29?
  34. 34.Is 3694 divisible by 15?
  35. 35.Is 111792 divisible by 17?
  36. 36.Is 66421 divisible by 13?
  37. 37.Is 210 divisible by 3?
  38. 38.Is 29590 divisible by 7?
  39. 39.Is 62117 divisible by 12?
  40. 40.Is 57593 divisible by 11?

Answer key

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

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