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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 267 · 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 120870 divisible by 30?
  2. 2.Is 74340 divisible by 20?
  3. 3.Is 54921 divisible by 12?
  4. 4.Is 165936 divisible by 24?
  5. 5.Is 66851 divisible by 30?
  6. 6.Is 159864 divisible by 24?
  7. 7.Is 3976 divisible by 5?
  8. 8.Is 109500 divisible by 30?
  9. 9.Is 76380 divisible by 19?
  10. 10.Is 34265 divisible by 11?
  11. 11.Is 24384 divisible by 6?
  12. 12.Is 20157 divisible by 6?
  13. 13.Is 13539 divisible by 9?
  14. 14.Is 126540 divisible by 30?
  15. 15.Is 12419 divisible by 29?
  16. 16.Is 36954 divisible by 6?
  17. 17.Is 125221 divisible by 29?
  18. 18.Is 37931 divisible by 19?
  19. 19.Is 20169 divisible by 3?
  20. 20.Is 43906 divisible by 29?
  21. 21.Is 78650 divisible by 13?
  22. 22.Is 1366 divisible by 5?
  23. 23.Is 43704 divisible by 8?
  24. 24.Is 28750 divisible by 18?
  25. 25.Is 45921 divisible by 13?
  26. 26.Is 48172 divisible by 9?
  27. 27.Is 71799 divisible by 29?
  28. 28.Is 23452 divisible by 11?
  29. 29.Is 10352 divisible by 2?
  30. 30.Is 14964 divisible by 4?
  31. 31.Is 115685 divisible by 17?
  32. 32.Is 5997 divisible by 3?
  33. 33.Is 57035 divisible by 9?
  34. 34.Is 10512 divisible by 2?
  35. 35.Is 29410 divisible by 6?
  36. 36.Is 65002 divisible by 30?
  37. 37.Is 1992 divisible by 3?
  38. 38.Is 6153 divisible by 2?
  39. 39.Is 6354 divisible by 9?
  40. 40.Is 76244 divisible by 15?

Answer key

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

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