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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 480 · 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 31857 divisible by 18?
  2. 2.Is 59808 divisible by 12?
  3. 3.Is 22440 divisible by 4?
  4. 4.Is 8274 divisible by 2?
  5. 5.Is 6800 divisible by 17?
  6. 6.Is 58792 divisible by 30?
  7. 7.Is 55482 divisible by 9?
  8. 8.Is 11601 divisible by 5?
  9. 9.Is 5387 divisible by 8?
  10. 10.Is 13021 divisible by 29?
  11. 11.Is 71668 divisible by 19?
  12. 12.Is 6849 divisible by 4?
  13. 13.Is 9622 divisible by 4?
  14. 14.Is 30918 divisible by 13?
  15. 15.Is 111725 divisible by 20?
  16. 16.Is 5140 divisible by 3?
  17. 17.Is 44606 divisible by 9?
  18. 18.Is 1292 divisible by 2?
  19. 19.Is 36821 divisible by 6?
  20. 20.Is 27946 divisible by 8?
  21. 21.Is 7211 divisible by 3?
  22. 22.Is 59664 divisible by 12?
  23. 23.Is 1166 divisible by 2?
  24. 24.Is 33262 divisible by 6?
  25. 25.Is 25110 divisible by 5?
  26. 26.Is 12857 divisible by 8?
  27. 27.Is 2212 divisible by 12?
  28. 28.Is 59562 divisible by 18?
  29. 29.Is 14450 divisible by 10?
  30. 30.Is 52704 divisible by 8?
  31. 31.Is 34275 divisible by 5?
  32. 32.Is 1589 divisible by 2?
  33. 33.Is 12940 divisible by 9?
  34. 34.Is 5769 divisible by 8?
  35. 35.Is 13871 divisible by 11?
  36. 36.Is 124434 divisible by 18?
  37. 37.Is 6245 divisible by 4?
  38. 38.Is 19692 divisible by 18?
  39. 39.Is 85847 divisible by 15?
  40. 40.Is 120492 divisible by 18?

Answer key

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

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