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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 671 · 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 20658 divisible by 11?
  2. 2.Is 39349 divisible by 7?
  3. 3.Is 74118 divisible by 19?
  4. 4.Is 78981 divisible by 23?
  5. 5.Is 26244 divisible by 4?
  6. 6.Is 48944 divisible by 7?
  7. 7.Is 145159 divisible by 23?
  8. 8.Is 9473 divisible by 4?
  9. 9.Is 15818 divisible by 9?
  10. 10.Is 40802 divisible by 23?
  11. 11.Is 7629 divisible by 2?
  12. 12.Is 3048 divisible by 4?
  13. 13.Is 15767 divisible by 19?
  14. 14.Is 28111 divisible by 11?
  15. 15.Is 22542 divisible by 6?
  16. 16.Is 37634 divisible by 23?
  17. 17.Is 5945 divisible by 8?
  18. 18.Is 6159 divisible by 6?
  19. 19.Is 26861 divisible by 17?
  20. 20.Is 98011 divisible by 18?
  21. 21.Is 37357 divisible by 6?
  22. 22.Is 34850 divisible by 5?
  23. 23.Is 4215 divisible by 5?
  24. 24.Is 47116 divisible by 30?
  25. 25.Is 10041 divisible by 5?
  26. 26.Is 23170 divisible by 10?
  27. 27.Is 58779 divisible by 9?
  28. 28.Is 42036 divisible by 9?
  29. 29.Is 12944 divisible by 8?
  30. 30.Is 43203 divisible by 24?
  31. 31.Is 48440 divisible by 8?
  32. 32.Is 134350 divisible by 20?
  33. 33.Is 38107 divisible by 6?
  34. 34.Is 32472 divisible by 9?
  35. 35.Is 61481 divisible by 10?
  36. 36.Is 94176 divisible by 18?
  37. 37.Is 16550 divisible by 10?
  38. 38.Is 144274 divisible by 29?
  39. 39.Is 119424 divisible by 20?
  40. 40.Is 55530 divisible by 30?

Answer key

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

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