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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 592 · 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 44996 divisible by 7?
  2. 2.Is 22120 divisible by 7?
  3. 3.Is 60946 divisible by 11?
  4. 4.Is 18732 divisible by 6?
  5. 5.Is 38700 divisible by 18?
  6. 6.Is 100042 divisible by 30?
  7. 7.Is 61446 divisible by 23?
  8. 8.Is 942 divisible by 3?
  9. 9.Is 42067 divisible by 12?
  10. 10.Is 16159 divisible by 13?
  11. 11.Is 84436 divisible by 24?
  12. 12.Is 39382 divisible by 7?
  13. 13.Is 8726 divisible by 2?
  14. 14.Is 33704 divisible by 8?
  15. 15.Is 22550 divisible by 13?
  16. 16.Is 12133 divisible by 4?
  17. 17.Is 71114 divisible by 13?
  18. 18.Is 17400 divisible by 3?
  19. 19.Is 24816 divisible by 7?
  20. 20.Is 10057 divisible by 13?
  21. 21.Is 4532 divisible by 2?
  22. 22.Is 105664 divisible by 19?
  23. 23.Is 17108 divisible by 5?
  24. 24.Is 105573 divisible by 17?
  25. 25.Is 52788 divisible by 12?
  26. 26.Is 11413 divisible by 9?
  27. 27.Is 13923 divisible by 7?
  28. 28.Is 9392 divisible by 2?
  29. 29.Is 32773 divisible by 19?
  30. 30.Is 4320 divisible by 4?
  31. 31.Is 20939 divisible by 4?
  32. 32.Is 175010 divisible by 30?
  33. 33.Is 32550 divisible by 17?
  34. 34.Is 2142 divisible by 10?
  35. 35.Is 28182 divisible by 11?
  36. 36.Is 5034 divisible by 6?
  37. 37.Is 107097 divisible by 29?
  38. 38.Is 10525 divisible by 6?
  39. 39.Is 2122 divisible by 23?
  40. 40.Is 18947 divisible by 8?

Answer key

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

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