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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 338 · 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 1641 divisible by 15?
  2. 2.Is 39693 divisible by 9?
  3. 3.Is 12264 divisible by 2?
  4. 4.Is 175209 divisible by 30?
  5. 5.Is 44815 divisible by 11?
  6. 6.Is 897 divisible by 4?
  7. 7.Is 11071 divisible by 30?
  8. 8.Is 1584 divisible by 8?
  9. 9.Is 22656 divisible by 24?
  10. 10.Is 55800 divisible by 9?
  11. 11.Is 20772 divisible by 20?
  12. 12.Is 34798 divisible by 8?
  13. 13.Is 1799 divisible by 6?
  14. 14.Is 24939 divisible by 5?
  15. 15.Is 74783 divisible by 17?
  16. 16.Is 88140 divisible by 13?
  17. 17.Is 125580 divisible by 30?
  18. 18.Is 10236 divisible by 7?
  19. 19.Is 72545 divisible by 23?
  20. 20.Is 1966 divisible by 3?
  21. 21.Is 56115 divisible by 15?
  22. 22.Is 27590 divisible by 24?
  23. 23.Is 21660 divisible by 6?
  24. 24.Is 130736 divisible by 20?
  25. 25.Is 1938 divisible by 6?
  26. 26.Is 13374 divisible by 6?
  27. 27.Is 16049 divisible by 11?
  28. 28.Is 106217 divisible by 20?
  29. 29.Is 15691 divisible by 17?
  30. 30.Is 9361 divisible by 11?
  31. 31.Is 17120 divisible by 10?
  32. 32.Is 3116 divisible by 5?
  33. 33.Is 12535 divisible by 5?
  34. 34.Is 9973 divisible by 2?
  35. 35.Is 7353 divisible by 9?
  36. 36.Is 18912 divisible by 6?
  37. 37.Is 71203 divisible by 23?
  38. 38.Is 60648 divisible by 20?
  39. 39.Is 11466 divisible by 18?
  40. 40.Is 22575 divisible by 20?

Answer key

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

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