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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 386 · 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 16312 divisible by 7?
  2. 2.Is 153750 divisible by 30?
  3. 3.Is 82440 divisible by 30?
  4. 4.Is 6576 divisible by 24?
  5. 5.Is 33541 divisible by 8?
  6. 6.Is 30335 divisible by 19?
  7. 7.Is 81630 divisible by 30?
  8. 8.Is 71766 divisible by 18?
  9. 9.Is 16854 divisible by 8?
  10. 10.Is 131974 divisible by 19?
  11. 11.Is 25242 divisible by 7?
  12. 12.Is 13234 divisible by 3?
  13. 13.Is 63917 divisible by 23?
  14. 14.Is 1259 divisible by 4?
  15. 15.Is 122245 divisible by 19?
  16. 16.Is 10560 divisible by 12?
  17. 17.Is 31399 divisible by 17?
  18. 18.Is 24614 divisible by 7?
  19. 19.Is 12397 divisible by 19?
  20. 20.Is 12276 divisible by 4?
  21. 21.Is 15128 divisible by 9?
  22. 22.Is 20815 divisible by 20?
  23. 23.Is 18663 divisible by 3?
  24. 24.Is 39280 divisible by 23?
  25. 25.Is 10198 divisible by 7?
  26. 26.Is 66663 divisible by 11?
  27. 27.Is 36290 divisible by 20?
  28. 28.Is 24437 divisible by 7?
  29. 29.Is 11033 divisible by 2?
  30. 30.Is 4236 divisible by 3?
  31. 31.Is 54630 divisible by 30?
  32. 32.Is 8104 divisible by 2?
  33. 33.Is 98590 divisible by 20?
  34. 34.Is 148697 divisible by 30?
  35. 35.Is 106776 divisible by 18?
  36. 36.Is 51480 divisible by 18?
  37. 37.Is 57624 divisible by 12?
  38. 38.Is 30852 divisible by 18?
  39. 39.Is 51456 divisible by 8?
  40. 40.Is 19420 divisible by 10?

Answer key

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

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