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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 664 · 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 16740 divisible by 15?
  2. 2.Is 26727 divisible by 5?
  3. 3.Is 2698 divisible by 19?
  4. 4.Is 184530 divisible by 30?
  5. 5.Is 4399 divisible by 6?
  6. 6.Is 51112 divisible by 8?
  7. 7.Is 152144 divisible by 24?
  8. 8.Is 87030 divisible by 30?
  9. 9.Is 7731 divisible by 13?
  10. 10.Is 111375 divisible by 17?
  11. 11.Is 75051 divisible by 13?
  12. 12.Is 2489 divisible by 20?
  13. 13.Is 25075 divisible by 6?
  14. 14.Is 195 divisible by 5?
  15. 15.Is 155814 divisible by 24?
  16. 16.Is 4401 divisible by 4?
  17. 17.Is 15609 divisible by 4?
  18. 18.Is 8640 divisible by 12?
  19. 19.Is 45965 divisible by 29?
  20. 20.Is 9762 divisible by 6?
  21. 21.Is 39207 divisible by 9?
  22. 22.Is 33570 divisible by 5?
  23. 23.Is 8087 divisible by 19?
  24. 24.Is 43810 divisible by 8?
  25. 25.Is 28433 divisible by 12?
  26. 26.Is 117419 divisible by 23?
  27. 27.Is 6561 divisible by 2?
  28. 28.Is 49022 divisible by 17?
  29. 29.Is 27496 divisible by 5?
  30. 30.Is 11208 divisible by 3?
  31. 31.Is 18402 divisible by 20?
  32. 32.Is 2489 divisible by 19?
  33. 33.Is 21805 divisible by 5?
  34. 34.Is 5804 divisible by 12?
  35. 35.Is 17915 divisible by 3?
  36. 36.Is 37072 divisible by 7?
  37. 37.Is 18827 divisible by 9?
  38. 38.Is 9059 divisible by 2?
  39. 39.Is 11595 divisible by 3?
  40. 40.Is 105706 divisible by 17?

Answer key

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

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