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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 120 · 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 1491 divisible by 7?
  2. 2.Is 79901 divisible by 20?
  3. 3.Is 7578 divisible by 4?
  4. 4.Is 23865 divisible by 4?
  5. 5.Is 95040 divisible by 30?
  6. 6.Is 47687 divisible by 8?
  7. 7.Is 44208 divisible by 11?
  8. 8.Is 17888 divisible by 3?
  9. 9.Is 104400 divisible by 15?
  10. 10.Is 17792 divisible by 3?
  11. 11.Is 1955 divisible by 17?
  12. 12.Is 3269 divisible by 7?
  13. 13.Is 12469 divisible by 15?
  14. 14.Is 21930 divisible by 5?
  15. 15.Is 2358 divisible by 2?
  16. 16.Is 2473 divisible by 3?
  17. 17.Is 23958 divisible by 6?
  18. 18.Is 4779 divisible by 17?
  19. 19.Is 99538 divisible by 18?
  20. 20.Is 65790 divisible by 18?
  21. 21.Is 65558 divisible by 12?
  22. 22.Is 11352 divisible by 6?
  23. 23.Is 139863 divisible by 23?
  24. 24.Is 10727 divisible by 2?
  25. 25.Is 35904 divisible by 8?
  26. 26.Is 8112 divisible by 13?
  27. 27.Is 14993 divisible by 13?
  28. 28.Is 70620 divisible by 20?
  29. 29.Is 4749 divisible by 2?
  30. 30.Is 35940 divisible by 6?
  31. 31.Is 95673 divisible by 15?
  32. 32.Is 38514 divisible by 7?
  33. 33.Is 6840 divisible by 10?
  34. 34.Is 32770 divisible by 5?
  35. 35.Is 21131 divisible by 17?
  36. 36.Is 2122 divisible by 15?
  37. 37.Is 6861 divisible by 3?
  38. 38.Is 10236 divisible by 11?
  39. 39.Is 13691 divisible by 3?
  40. 40.Is 8124 divisible by 2?

Answer key

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

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