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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 162 · 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 118276 divisible by 17?
  2. 2.Is 28923 divisible by 20?
  3. 3.Is 21056 divisible by 8?
  4. 4.Is 171941 divisible by 29?
  5. 5.Is 47579 divisible by 7?
  6. 6.Is 2020 divisible by 3?
  7. 7.Is 45739 divisible by 7?
  8. 8.Is 78706 divisible by 23?
  9. 9.Is 112102 divisible by 23?
  10. 10.Is 44544 divisible by 29?
  11. 11.Is 8600 divisible by 7?
  12. 12.Is 110561 divisible by 19?
  13. 13.Is 160564 divisible by 23?
  14. 14.Is 24302 divisible by 29?
  15. 15.Is 81840 divisible by 30?
  16. 16.Is 57084 divisible by 12?
  17. 17.Is 88445 divisible by 20?
  18. 18.Is 28077 divisible by 7?
  19. 19.Is 22052 divisible by 4?
  20. 20.Is 128975 divisible by 24?
  21. 21.Is 161244 divisible by 30?
  22. 22.Is 8240 divisible by 4?
  23. 23.Is 14421 divisible by 3?
  24. 24.Is 146682 divisible by 29?
  25. 25.Is 20730 divisible by 5?
  26. 26.Is 24584 divisible by 4?
  27. 27.Is 92205 divisible by 17?
  28. 28.Is 180583 divisible by 29?
  29. 29.Is 153795 divisible by 29?
  30. 30.Is 27680 divisible by 20?
  31. 31.Is 7771 divisible by 13?
  32. 32.Is 74658 divisible by 12?
  33. 33.Is 5435 divisible by 5?
  34. 34.Is 56775 divisible by 15?
  35. 35.Is 95243 divisible by 23?
  36. 36.Is 125534 divisible by 23?
  37. 37.Is 3712 divisible by 8?
  38. 38.Is 84141 divisible by 24?
  39. 39.Is 22762 divisible by 23?
  40. 40.Is 28304 divisible by 8?

Answer key

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

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