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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 251 · 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 120408 divisible by 24?
  2. 2.Is 10465 divisible by 2?
  3. 3.Is 97971 divisible by 17?
  4. 4.Is 62391 divisible by 17?
  5. 5.Is 11536 divisible by 4?
  6. 6.Is 4714 divisible by 11?
  7. 7.Is 6708 divisible by 2?
  8. 8.Is 190327 divisible by 29?
  9. 9.Is 122704 divisible by 24?
  10. 10.Is 41237 divisible by 7?
  11. 11.Is 8669 divisible by 3?
  12. 12.Is 86490 divisible by 13?
  13. 13.Is 22722 divisible by 13?
  14. 14.Is 40536 divisible by 29?
  15. 15.Is 70260 divisible by 20?
  16. 16.Is 3609 divisible by 9?
  17. 17.Is 34551 divisible by 11?
  18. 18.Is 99390 divisible by 30?
  19. 19.Is 5984 divisible by 17?
  20. 20.Is 5612 divisible by 23?
  21. 21.Is 2175 divisible by 7?
  22. 22.Is 33082 divisible by 17?
  23. 23.Is 40473 divisible by 9?
  24. 24.Is 73971 divisible by 20?
  25. 25.Is 47355 divisible by 7?
  26. 26.Is 20677 divisible by 23?
  27. 27.Is 56335 divisible by 10?
  28. 28.Is 92990 divisible by 17?
  29. 29.Is 3366 divisible by 3?
  30. 30.Is 40450 divisible by 8?
  31. 31.Is 45465 divisible by 15?
  32. 32.Is 15190 divisible by 7?
  33. 33.Is 52357 divisible by 8?
  34. 34.Is 14931 divisible by 6?
  35. 35.Is 24516 divisible by 12?
  36. 36.Is 130464 divisible by 24?
  37. 37.Is 62929 divisible by 9?
  38. 38.Is 60643 divisible by 29?
  39. 39.Is 74800 divisible by 17?
  40. 40.Is 37153 divisible by 24?

Answer key

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

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