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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 501 · 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 86360 divisible by 17?
  2. 2.Is 57096 divisible by 12?
  3. 3.Is 67562 divisible by 11?
  4. 4.Is 6980 divisible by 2?
  5. 5.Is 1990 divisible by 3?
  6. 6.Is 19551 divisible by 7?
  7. 7.Is 59556 divisible by 12?
  8. 8.Is 35684 divisible by 6?
  9. 9.Is 12725 divisible by 4?
  10. 10.Is 91876 divisible by 17?
  11. 11.Is 60678 divisible by 10?
  12. 12.Is 71649 divisible by 19?
  13. 13.Is 31763 divisible by 8?
  14. 14.Is 5736 divisible by 8?
  15. 15.Is 6734 divisible by 4?
  16. 16.Is 15813 divisible by 8?
  17. 17.Is 44936 divisible by 8?
  18. 18.Is 15265 divisible by 24?
  19. 19.Is 25342 divisible by 7?
  20. 20.Is 30668 divisible by 10?
  21. 21.Is 89586 divisible by 18?
  22. 22.Is 61846 divisible by 20?
  23. 23.Is 37813 divisible by 11?
  24. 24.Is 3140 divisible by 5?
  25. 25.Is 836 divisible by 6?
  26. 26.Is 43209 divisible by 7?
  27. 27.Is 59906 divisible by 11?
  28. 28.Is 7302 divisible by 4?
  29. 29.Is 48270 divisible by 10?
  30. 30.Is 10869 divisible by 3?
  31. 31.Is 34286 divisible by 5?
  32. 32.Is 16285 divisible by 3?
  33. 33.Is 17600 divisible by 11?
  34. 34.Is 50571 divisible by 15?
  35. 35.Is 21620 divisible by 10?
  36. 36.Is 45255 divisible by 7?
  37. 37.Is 86197 divisible by 24?
  38. 38.Is 11383 divisible by 2?
  39. 39.Is 34600 divisible by 5?
  40. 40.Is 110778 divisible by 18?

Answer key

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

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