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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 246 · 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 23665 divisible by 5?
  2. 2.Is 13217 divisible by 4?
  3. 3.Is 34764 divisible by 9?
  4. 4.Is 177510 divisible by 30?
  5. 5.Is 7757 divisible by 7?
  6. 6.Is 8551 divisible by 9?
  7. 7.Is 158456 divisible by 29?
  8. 8.Is 29824 divisible by 24?
  9. 9.Is 37830 divisible by 13?
  10. 10.Is 69004 divisible by 10?
  11. 11.Is 26628 divisible by 6?
  12. 12.Is 75255 divisible by 18?
  13. 13.Is 21541 divisible by 4?
  14. 14.Is 60318 divisible by 9?
  15. 15.Is 41337 divisible by 6?
  16. 16.Is 8467 divisible by 2?
  17. 17.Is 141513 divisible by 24?
  18. 18.Is 77880 divisible by 20?
  19. 19.Is 100803 divisible by 24?
  20. 20.Is 59050 divisible by 18?
  21. 21.Is 22170 divisible by 10?
  22. 22.Is 26943 divisible by 6?
  23. 23.Is 49922 divisible by 30?
  24. 24.Is 1724 divisible by 10?
  25. 25.Is 32351 divisible by 6?
  26. 26.Is 120005 divisible by 20?
  27. 27.Is 176220 divisible by 30?
  28. 28.Is 4888 divisible by 13?
  29. 29.Is 77040 divisible by 15?
  30. 30.Is 29412 divisible by 20?
  31. 31.Is 56574 divisible by 10?
  32. 32.Is 45418 divisible by 7?
  33. 33.Is 22290 divisible by 5?
  34. 34.Is 21532 divisible by 4?
  35. 35.Is 104550 divisible by 30?
  36. 36.Is 123636 divisible by 23?
  37. 37.Is 6194 divisible by 7?
  38. 38.Is 50355 divisible by 15?
  39. 39.Is 187423 divisible by 30?
  40. 40.Is 7572 divisible by 2?

Answer key

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

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