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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 411 · 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 19334 divisible by 3?
  2. 2.Is 53631 divisible by 20?
  3. 3.Is 16157 divisible by 6?
  4. 4.Is 58119 divisible by 11?
  5. 5.Is 56763 divisible by 9?
  6. 6.Is 58590 divisible by 20?
  7. 7.Is 8368 divisible by 8?
  8. 8.Is 31997 divisible by 7?
  9. 9.Is 103989 divisible by 17?
  10. 10.Is 22728 divisible by 8?
  11. 11.Is 11640 divisible by 30?
  12. 12.Is 57744 divisible by 18?
  13. 13.Is 30540 divisible by 10?
  14. 14.Is 28598 divisible by 10?
  15. 15.Is 122166 divisible by 18?
  16. 16.Is 53180 divisible by 20?
  17. 17.Is 98281 divisible by 29?
  18. 18.Is 46978 divisible by 11?
  19. 19.Is 133874 divisible by 23?
  20. 20.Is 15865 divisible by 19?
  21. 21.Is 1265 divisible by 4?
  22. 22.Is 8244 divisible by 4?
  23. 23.Is 2524 divisible by 4?
  24. 24.Is 7946 divisible by 5?
  25. 25.Is 35410 divisible by 18?
  26. 26.Is 864 divisible by 3?
  27. 27.Is 6725 divisible by 4?
  28. 28.Is 8685 divisible by 4?
  29. 29.Is 24578 divisible by 4?
  30. 30.Is 94440 divisible by 24?
  31. 31.Is 2275 divisible by 5?
  32. 32.Is 21144 divisible by 8?
  33. 33.Is 9668 divisible by 2?
  34. 34.Is 36316 divisible by 6?
  35. 35.Is 18883 divisible by 4?
  36. 36.Is 32655 divisible by 7?
  37. 37.Is 11520 divisible by 5?
  38. 38.Is 18489 divisible by 3?
  39. 39.Is 90280 divisible by 20?
  40. 40.Is 79848 divisible by 24?

Answer key

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

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