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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 795 · 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 62297 divisible by 15?
  2. 2.Is 26951 divisible by 17?
  3. 3.Is 22491 divisible by 7?
  4. 4.Is 26772 divisible by 29?
  5. 5.Is 116919 divisible by 17?
  6. 6.Is 2616 divisible by 12?
  7. 7.Is 8400 divisible by 15?
  8. 8.Is 5080 divisible by 4?
  9. 9.Is 34532 divisible by 5?
  10. 10.Is 94581 divisible by 19?
  11. 11.Is 92905 divisible by 17?
  12. 12.Is 13870 divisible by 2?
  13. 13.Is 2776 divisible by 9?
  14. 14.Is 4557 divisible by 2?
  15. 15.Is 62056 divisible by 17?
  16. 16.Is 160230 divisible by 23?
  17. 17.Is 19670 divisible by 5?
  18. 18.Is 24939 divisible by 17?
  19. 19.Is 58671 divisible by 24?
  20. 20.Is 156147 divisible by 23?
  21. 21.Is 17052 divisible by 12?
  22. 22.Is 60460 divisible by 29?
  23. 23.Is 21552 divisible by 24?
  24. 24.Is 156273 divisible by 29?
  25. 25.Is 90555 divisible by 15?
  26. 26.Is 643 divisible by 2?
  27. 27.Is 41420 divisible by 20?
  28. 28.Is 22636 divisible by 11?
  29. 29.Is 6768 divisible by 2?
  30. 30.Is 56052 divisible by 11?
  31. 31.Is 94323 divisible by 30?
  32. 32.Is 7593 divisible by 4?
  33. 33.Is 15599 divisible by 4?
  34. 34.Is 7450 divisible by 2?
  35. 35.Is 93555 divisible by 15?
  36. 36.Is 8373 divisible by 12?
  37. 37.Is 1691 divisible by 2?
  38. 38.Is 38583 divisible by 11?
  39. 39.Is 11452 divisible by 4?
  40. 40.Is 66240 divisible by 11?

Answer key

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

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