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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 398 · 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 43554 divisible by 7?
  2. 2.Is 42639 divisible by 17?
  3. 3.Is 7011 divisible by 9?
  4. 4.Is 111010 divisible by 17?
  5. 5.Is 47512 divisible by 8?
  6. 6.Is 8624 divisible by 2?
  7. 7.Is 35580 divisible by 20?
  8. 8.Is 2304 divisible by 4?
  9. 9.Is 26180 divisible by 7?
  10. 10.Is 55204 divisible by 8?
  11. 11.Is 9924 divisible by 2?
  12. 12.Is 26136 divisible by 11?
  13. 13.Is 30788 divisible by 10?
  14. 14.Is 35303 divisible by 8?
  15. 15.Is 21813 divisible by 13?
  16. 16.Is 68714 divisible by 13?
  17. 17.Is 23924 divisible by 4?
  18. 18.Is 6759 divisible by 2?
  19. 19.Is 22165 divisible by 9?
  20. 20.Is 8227 divisible by 19?
  21. 21.Is 13399 divisible by 9?
  22. 22.Is 33276 divisible by 12?
  23. 23.Is 67679 divisible by 10?
  24. 24.Is 42820 divisible by 20?
  25. 25.Is 34368 divisible by 7?
  26. 26.Is 5524 divisible by 2?
  27. 27.Is 56955 divisible by 9?
  28. 28.Is 21589 divisible by 4?
  29. 29.Is 10244 divisible by 13?
  30. 30.Is 21119 divisible by 4?
  31. 31.Is 6517 divisible by 4?
  32. 32.Is 38799 divisible by 9?
  33. 33.Is 12809 divisible by 6?
  34. 34.Is 13352 divisible by 3?
  35. 35.Is 9560 divisible by 8?
  36. 36.Is 10940 divisible by 4?
  37. 37.Is 6946 divisible by 2?
  38. 38.Is 53870 divisible by 11?
  39. 39.Is 153900 divisible by 30?
  40. 40.Is 20460 divisible by 10?

Answer key

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

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