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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 772 · 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 19671 divisible by 4?
  2. 2.Is 81761 divisible by 15?
  3. 3.Is 55838 divisible by 20?
  4. 4.Is 22473 divisible by 10?
  5. 5.Is 3074 divisible by 2?
  6. 6.Is 16536 divisible by 8?
  7. 7.Is 4864 divisible by 6?
  8. 8.Is 3865 divisible by 2?
  9. 9.Is 43584 divisible by 8?
  10. 10.Is 31780 divisible by 5?
  11. 11.Is 61856 divisible by 13?
  12. 12.Is 46878 divisible by 12?
  13. 13.Is 20490 divisible by 3?
  14. 14.Is 16989 divisible by 11?
  15. 15.Is 33124 divisible by 7?
  16. 16.Is 3225 divisible by 3?
  17. 17.Is 124128 divisible by 18?
  18. 18.Is 18706 divisible by 11?
  19. 19.Is 14842 divisible by 7?
  20. 20.Is 4685 divisible by 5?
  21. 21.Is 159436 divisible by 29?
  22. 22.Is 44114 divisible by 7?
  23. 23.Is 131910 divisible by 30?
  24. 24.Is 20004 divisible by 12?
  25. 25.Is 8886 divisible by 17?
  26. 26.Is 18072 divisible by 10?
  27. 27.Is 103407 divisible by 20?
  28. 28.Is 8436 divisible by 6?
  29. 29.Is 7723 divisible by 20?
  30. 30.Is 9742 divisible by 5?
  31. 31.Is 39258 divisible by 12?
  32. 32.Is 11507 divisible by 3?
  33. 33.Is 125372 divisible by 18?
  34. 34.Is 36976 divisible by 6?
  35. 35.Is 11806 divisible by 3?
  36. 36.Is 27724 divisible by 8?
  37. 37.Is 100600 divisible by 20?
  38. 38.Is 20199 divisible by 5?
  39. 39.Is 22244 divisible by 6?
  40. 40.Is 139320 divisible by 20?

Answer key

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

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