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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 3 · 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 38176 divisible by 8?
  2. 2.Is 6997 divisible by 4?
  3. 3.Is 7805 divisible by 4?
  4. 4.Is 21701 divisible by 4?
  5. 5.Is 9342 divisible by 18?
  6. 6.Is 100260 divisible by 30?
  7. 7.Is 26569 divisible by 23?
  8. 8.Is 22912 divisible by 8?
  9. 9.Is 29748 divisible by 5?
  10. 10.Is 2460 divisible by 10?
  11. 11.Is 4299 divisible by 6?
  12. 12.Is 771 divisible by 5?
  13. 13.Is 155350 divisible by 24?
  14. 14.Is 66031 divisible by 30?
  15. 15.Is 61794 divisible by 18?
  16. 16.Is 51428 divisible by 13?
  17. 17.Is 6695 divisible by 3?
  18. 18.Is 76995 divisible by 15?
  19. 19.Is 13594 divisible by 8?
  20. 20.Is 6159 divisible by 3?
  21. 21.Is 43800 divisible by 20?
  22. 22.Is 41092 divisible by 7?
  23. 23.Is 2410 divisible by 8?
  24. 24.Is 38797 divisible by 7?
  25. 25.Is 19647 divisible by 30?
  26. 26.Is 73596 divisible by 17?
  27. 27.Is 21140 divisible by 10?
  28. 28.Is 65230 divisible by 11?
  29. 29.Is 20922 divisible by 3?
  30. 30.Is 12760 divisible by 20?
  31. 31.Is 112628 divisible by 20?
  32. 32.Is 37930 divisible by 23?
  33. 33.Is 15733 divisible by 6?
  34. 34.Is 1594 divisible by 2?
  35. 35.Is 50004 divisible by 18?
  36. 36.Is 18354 divisible by 19?
  37. 37.Is 102561 divisible by 15?
  38. 38.Is 20527 divisible by 12?
  39. 39.Is 132536 divisible by 19?
  40. 40.Is 4444 divisible by 30?

Answer key

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

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