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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 416 · 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 7937 divisible by 4?
  2. 2.Is 13998 divisible by 5?
  3. 3.Is 55772 divisible by 11?
  4. 4.Is 10334 divisible by 2?
  5. 5.Is 107111 divisible by 23?
  6. 6.Is 2303 divisible by 7?
  7. 7.Is 9319 divisible by 6?
  8. 8.Is 56279 divisible by 17?
  9. 9.Is 62890 divisible by 11?
  10. 10.Is 39190 divisible by 18?
  11. 11.Is 155983 divisible by 23?
  12. 12.Is 21616 divisible by 8?
  13. 13.Is 2868 divisible by 3?
  14. 14.Is 42207 divisible by 10?
  15. 15.Is 1366 divisible by 19?
  16. 16.Is 3758 divisible by 3?
  17. 17.Is 12925 divisible by 5?
  18. 18.Is 91807 divisible by 29?
  19. 19.Is 12341 divisible by 5?
  20. 20.Is 9380 divisible by 20?
  21. 21.Is 59223 divisible by 20?
  22. 22.Is 15321 divisible by 5?
  23. 23.Is 20701 divisible by 3?
  24. 24.Is 3080 divisible by 4?
  25. 25.Is 104574 divisible by 29?
  26. 26.Is 12825 divisible by 5?
  27. 27.Is 90896 divisible by 18?
  28. 28.Is 3540 divisible by 15?
  29. 29.Is 44358 divisible by 29?
  30. 30.Is 79439 divisible by 19?
  31. 31.Is 71129 divisible by 18?
  32. 32.Is 7035 divisible by 7?
  33. 33.Is 110826 divisible by 18?
  34. 34.Is 15574 divisible by 3?
  35. 35.Is 21857 divisible by 11?
  36. 36.Is 174540 divisible by 30?
  37. 37.Is 25484 divisible by 8?
  38. 38.Is 150397 divisible by 23?
  39. 39.Is 5802 divisible by 10?
  40. 40.Is 260 divisible by 4?

Answer key

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

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