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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 798 · 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 16381 divisible by 13?
  2. 2.Is 77 divisible by 2?
  3. 3.Is 50354 divisible by 13?
  4. 4.Is 74738 divisible by 17?
  5. 5.Is 5594 divisible by 7?
  6. 6.Is 4750 divisible by 5?
  7. 7.Is 21936 divisible by 17?
  8. 8.Is 17638 divisible by 8?
  9. 9.Is 135431 divisible by 23?
  10. 10.Is 44428 divisible by 29?
  11. 11.Is 109087 divisible by 23?
  12. 12.Is 49500 divisible by 15?
  13. 13.Is 9783 divisible by 2?
  14. 14.Is 25109 divisible by 17?
  15. 15.Is 44037 divisible by 7?
  16. 16.Is 8358 divisible by 2?
  17. 17.Is 1683 divisible by 17?
  18. 18.Is 53592 divisible by 10?
  19. 19.Is 63130 divisible by 13?
  20. 20.Is 80847 divisible by 20?
  21. 21.Is 11730 divisible by 30?
  22. 22.Is 29085 divisible by 17?
  23. 23.Is 14099 divisible by 3?
  24. 24.Is 5897 divisible by 3?
  25. 25.Is 11586 divisible by 2?
  26. 26.Is 45022 divisible by 8?
  27. 27.Is 957 divisible by 3?
  28. 28.Is 38511 divisible by 19?
  29. 29.Is 129640 divisible by 20?
  30. 30.Is 19763 divisible by 7?
  31. 31.Is 24635 divisible by 13?
  32. 32.Is 27209 divisible by 23?
  33. 33.Is 2168 divisible by 19?
  34. 34.Is 33208 divisible by 8?
  35. 35.Is 11610 divisible by 15?
  36. 36.Is 73350 divisible by 18?
  37. 37.Is 48942 divisible by 18?
  38. 38.Is 2496 divisible by 3?
  39. 39.Is 125164 divisible by 19?
  40. 40.Is 110403 divisible by 20?

Answer key

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

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