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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 647 · 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 60228 divisible by 12?
  2. 2.Is 7536 divisible by 2?
  3. 3.Is 1545 divisible by 4?
  4. 4.Is 77250 divisible by 30?
  5. 5.Is 15332 divisible by 5?
  6. 6.Is 141551 divisible by 23?
  7. 7.Is 123156 divisible by 18?
  8. 8.Is 10577 divisible by 7?
  9. 9.Is 6127 divisible by 17?
  10. 10.Is 29219 divisible by 20?
  11. 11.Is 23855 divisible by 13?
  12. 12.Is 538 divisible by 19?
  13. 13.Is 134460 divisible by 30?
  14. 14.Is 38322 divisible by 24?
  15. 15.Is 40420 divisible by 10?
  16. 16.Is 6096 divisible by 3?
  17. 17.Is 580 divisible by 20?
  18. 18.Is 18645 divisible by 17?
  19. 19.Is 2494 divisible by 7?
  20. 20.Is 150630 divisible by 30?
  21. 21.Is 73138 divisible by 13?
  22. 22.Is 33362 divisible by 7?
  23. 23.Is 27384 divisible by 24?
  24. 24.Is 9455 divisible by 2?
  25. 25.Is 11442 divisible by 2?
  26. 26.Is 101264 divisible by 24?
  27. 27.Is 7183 divisible by 30?
  28. 28.Is 33902 divisible by 23?
  29. 29.Is 98505 divisible by 17?
  30. 30.Is 71404 divisible by 19?
  31. 31.Is 94863 divisible by 20?
  32. 32.Is 12603 divisible by 23?
  33. 33.Is 63308 divisible by 19?
  34. 34.Is 1264 divisible by 4?
  35. 35.Is 116008 divisible by 17?
  36. 36.Is 73271 divisible by 23?
  37. 37.Is 28938 divisible by 7?
  38. 38.Is 31618 divisible by 6?
  39. 39.Is 61449 divisible by 9?
  40. 40.Is 36345 divisible by 19?

Answer key

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

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