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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 498 · 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 84176 divisible by 18?
  2. 2.Is 22572 divisible by 9?
  3. 3.Is 67955 divisible by 18?
  4. 4.Is 12158 divisible by 3?
  5. 5.Is 5086 divisible by 10?
  6. 6.Is 2285 divisible by 6?
  7. 7.Is 60878 divisible by 24?
  8. 8.Is 73454 divisible by 19?
  9. 9.Is 34353 divisible by 5?
  10. 10.Is 9967 divisible by 4?
  11. 11.Is 42573 divisible by 23?
  12. 12.Is 32104 divisible by 8?
  13. 13.Is 44779 divisible by 7?
  14. 14.Is 8584 divisible by 29?
  15. 15.Is 12437 divisible by 9?
  16. 16.Is 172184 divisible by 29?
  17. 17.Is 128212 divisible by 19?
  18. 18.Is 24931 divisible by 7?
  19. 19.Is 45284 divisible by 15?
  20. 20.Is 6884 divisible by 20?
  21. 21.Is 5010 divisible by 2?
  22. 22.Is 20354 divisible by 24?
  23. 23.Is 148152 divisible by 24?
  24. 24.Is 70411 divisible by 23?
  25. 25.Is 23577 divisible by 4?
  26. 26.Is 4368 divisible by 4?
  27. 27.Is 72630 divisible by 15?
  28. 28.Is 43357 divisible by 18?
  29. 29.Is 39572 divisible by 13?
  30. 30.Is 32894 divisible by 13?
  31. 31.Is 26647 divisible by 6?
  32. 32.Is 25336 divisible by 5?
  33. 33.Is 28274 divisible by 5?
  34. 34.Is 9604 divisible by 8?
  35. 35.Is 3750 divisible by 30?
  36. 36.Is 2041 divisible by 2?
  37. 37.Is 16548 divisible by 3?
  38. 38.Is 168300 divisible by 30?
  39. 39.Is 35320 divisible by 20?
  40. 40.Is 105820 divisible by 20?

Answer key

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

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