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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 302 · 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 17870 divisible by 10?
  2. 2.Is 114559 divisible by 19?
  3. 3.Is 37370 divisible by 10?
  4. 4.Is 17688 divisible by 24?
  5. 5.Is 17505 divisible by 15?
  6. 6.Is 38680 divisible by 20?
  7. 7.Is 74052 divisible by 15?
  8. 8.Is 9558 divisible by 18?
  9. 9.Is 161208 divisible by 24?
  10. 10.Is 80418 divisible by 23?
  11. 11.Is 31040 divisible by 8?
  12. 12.Is 55807 divisible by 29?
  13. 13.Is 33776 divisible by 12?
  14. 14.Is 114660 divisible by 19?
  15. 15.Is 10472 divisible by 8?
  16. 16.Is 1432 divisible by 4?
  17. 17.Is 17354 divisible by 7?
  18. 18.Is 1968 divisible by 13?
  19. 19.Is 980 divisible by 4?
  20. 20.Is 8723 divisible by 11?
  21. 21.Is 110256 divisible by 24?
  22. 22.Is 98118 divisible by 18?
  23. 23.Is 41700 divisible by 15?
  24. 24.Is 26645 divisible by 5?
  25. 25.Is 80115 divisible by 12?
  26. 26.Is 136186 divisible by 23?
  27. 27.Is 67454 divisible by 13?
  28. 28.Is 60578 divisible by 9?
  29. 29.Is 55302 divisible by 13?
  30. 30.Is 32019 divisible by 11?
  31. 31.Is 27308 divisible by 15?
  32. 32.Is 147975 divisible by 23?
  33. 33.Is 70156 divisible by 20?
  34. 34.Is 5759 divisible by 2?
  35. 35.Is 7175 divisible by 3?
  36. 36.Is 25956 divisible by 15?
  37. 37.Is 9936 divisible by 6?
  38. 38.Is 10240 divisible by 8?
  39. 39.Is 5879 divisible by 2?
  40. 40.Is 38148 divisible by 29?

Answer key

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

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