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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 520 · 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 3535 divisible by 6?
  2. 2.Is 5194 divisible by 7?
  3. 3.Is 3894 divisible by 5?
  4. 4.Is 47832 divisible by 12?
  5. 5.Is 105402 divisible by 17?
  6. 6.Is 19350 divisible by 3?
  7. 7.Is 115260 divisible by 20?
  8. 8.Is 117508 divisible by 29?
  9. 9.Is 116263 divisible by 29?
  10. 10.Is 5015 divisible by 2?
  11. 11.Is 191958 divisible by 29?
  12. 12.Is 22842 divisible by 4?
  13. 13.Is 57072 divisible by 12?
  14. 14.Is 86337 divisible by 18?
  15. 15.Is 39607 divisible by 18?
  16. 16.Is 19123 divisible by 5?
  17. 17.Is 3541 divisible by 2?
  18. 18.Is 32162 divisible by 13?
  19. 19.Is 19166 divisible by 3?
  20. 20.Is 9262 divisible by 11?
  21. 21.Is 94600 divisible by 20?
  22. 22.Is 89674 divisible by 24?
  23. 23.Is 32109 divisible by 11?
  24. 24.Is 15778 divisible by 23?
  25. 25.Is 1998 divisible by 7?
  26. 26.Is 31103 divisible by 24?
  27. 27.Is 28867 divisible by 11?
  28. 28.Is 35101 divisible by 11?
  29. 29.Is 12888 divisible by 6?
  30. 30.Is 14436 divisible by 18?
  31. 31.Is 19561 divisible by 20?
  32. 32.Is 24390 divisible by 7?
  33. 33.Is 86122 divisible by 17?
  34. 34.Is 25776 divisible by 18?
  35. 35.Is 38640 divisible by 12?
  36. 36.Is 49161 divisible by 12?
  37. 37.Is 23576 divisible by 4?
  38. 38.Is 11195 divisible by 10?
  39. 39.Is 2621 divisible by 4?
  40. 40.Is 3045 divisible by 2?

Answer key

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

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