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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 46 · 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 154146 divisible by 23?
  2. 2.Is 48950 divisible by 30?
  3. 3.Is 32250 divisible by 7?
  4. 4.Is 100174 divisible by 29?
  5. 5.Is 20328 divisible by 3?
  6. 6.Is 14616 divisible by 8?
  7. 7.Is 12002 divisible by 20?
  8. 8.Is 93364 divisible by 23?
  9. 9.Is 32318 divisible by 13?
  10. 10.Is 9890 divisible by 10?
  11. 11.Is 79360 divisible by 20?
  12. 12.Is 20478 divisible by 7?
  13. 13.Is 35849 divisible by 11?
  14. 14.Is 3329 divisible by 3?
  15. 15.Is 7985 divisible by 5?
  16. 16.Is 49161 divisible by 19?
  17. 17.Is 50796 divisible by 12?
  18. 18.Is 10352 divisible by 2?
  19. 19.Is 44805 divisible by 15?
  20. 20.Is 150727 divisible by 24?
  21. 21.Is 131211 divisible by 23?
  22. 22.Is 11818 divisible by 4?
  23. 23.Is 30328 divisible by 9?
  24. 24.Is 35380 divisible by 20?
  25. 25.Is 54323 divisible by 10?
  26. 26.Is 16465 divisible by 5?
  27. 27.Is 5772 divisible by 7?
  28. 28.Is 149280 divisible by 30?
  29. 29.Is 46851 divisible by 23?
  30. 30.Is 1278 divisible by 6?
  31. 31.Is 3143 divisible by 2?
  32. 32.Is 39536 divisible by 7?
  33. 33.Is 15251 divisible by 11?
  34. 34.Is 171517 divisible by 30?
  35. 35.Is 95760 divisible by 20?
  36. 36.Is 6174 divisible by 20?
  37. 37.Is 43208 divisible by 8?
  38. 38.Is 13731 divisible by 2?
  39. 39.Is 52598 divisible by 17?
  40. 40.Is 96298 divisible by 23?

Answer key

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

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