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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 45 · 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 48270 divisible by 30?
  2. 2.Is 15860 divisible by 10?
  3. 3.Is 26000 divisible by 8?
  4. 4.Is 65458 divisible by 23?
  5. 5.Is 23121 divisible by 9?
  6. 6.Is 39860 divisible by 17?
  7. 7.Is 24369 divisible by 9?
  8. 8.Is 121803 divisible by 24?
  9. 9.Is 10616 divisible by 12?
  10. 10.Is 106726 divisible by 17?
  11. 11.Is 154800 divisible by 24?
  12. 12.Is 16440 divisible by 6?
  13. 13.Is 22920 divisible by 10?
  14. 14.Is 30492 divisible by 18?
  15. 15.Is 45 divisible by 2?
  16. 16.Is 9945 divisible by 2?
  17. 17.Is 40358 divisible by 6?
  18. 18.Is 32751 divisible by 5?
  19. 19.Is 42660 divisible by 10?
  20. 20.Is 1050 divisible by 15?
  21. 21.Is 32581 divisible by 8?
  22. 22.Is 103979 divisible by 18?
  23. 23.Is 5456 divisible by 5?
  24. 24.Is 22378 divisible by 6?
  25. 25.Is 46092 divisible by 23?
  26. 26.Is 20740 divisible by 12?
  27. 27.Is 34980 divisible by 20?
  28. 28.Is 56800 divisible by 20?
  29. 29.Is 23288 divisible by 12?
  30. 30.Is 21990 divisible by 5?
  31. 31.Is 14075 divisible by 30?
  32. 32.Is 33817 divisible by 7?
  33. 33.Is 10080 divisible by 20?
  34. 34.Is 25957 divisible by 13?
  35. 35.Is 27024 divisible by 6?
  36. 36.Is 40369 divisible by 15?
  37. 37.Is 5702 divisible by 24?
  38. 38.Is 78408 divisible by 18?
  39. 39.Is 33592 divisible by 10?
  40. 40.Is 44554 divisible by 7?

Answer key

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

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