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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 896 · 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 156745 divisible by 23?
  2. 2.Is 29554 divisible by 13?
  3. 3.Is 2244 divisible by 17?
  4. 4.Is 9160 divisible by 10?
  5. 5.Is 44142 divisible by 7?
  6. 6.Is 60255 divisible by 20?
  7. 7.Is 16159 divisible by 3?
  8. 8.Is 144630 divisible by 30?
  9. 9.Is 21140 divisible by 4?
  10. 10.Is 23604 divisible by 4?
  11. 11.Is 26984 divisible by 20?
  12. 12.Is 41829 divisible by 10?
  13. 13.Is 20049 divisible by 3?
  14. 14.Is 91998 divisible by 19?
  15. 15.Is 54914 divisible by 30?
  16. 16.Is 12750 divisible by 10?
  17. 17.Is 64331 divisible by 23?
  18. 18.Is 52171 divisible by 29?
  19. 19.Is 2437 divisible by 2?
  20. 20.Is 61761 divisible by 17?
  21. 21.Is 18917 divisible by 6?
  22. 22.Is 8833 divisible by 11?
  23. 23.Is 90644 divisible by 17?
  24. 24.Is 6533 divisible by 9?
  25. 25.Is 42249 divisible by 7?
  26. 26.Is 9300 divisible by 4?
  27. 27.Is 68000 divisible by 10?
  28. 28.Is 128910 divisible by 30?
  29. 29.Is 24721 divisible by 4?
  30. 30.Is 171740 divisible by 29?
  31. 31.Is 66240 divisible by 10?
  32. 32.Is 49239 divisible by 11?
  33. 33.Is 27180 divisible by 9?
  34. 34.Is 3300 divisible by 30?
  35. 35.Is 16701 divisible by 4?
  36. 36.Is 6440 divisible by 29?
  37. 37.Is 109703 divisible by 18?
  38. 38.Is 4324 divisible by 3?
  39. 39.Is 8216 divisible by 4?
  40. 40.Is 105103 divisible by 23?

Answer key

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

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