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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 16 · 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 59559 divisible by 10?
  2. 2.Is 55379 divisible by 17?
  3. 3.Is 1978 divisible by 11?
  4. 4.Is 28410 divisible by 11?
  5. 5.Is 12195 divisible by 2?
  6. 6.Is 26786 divisible by 4?
  7. 7.Is 70879 divisible by 15?
  8. 8.Is 8223 divisible by 3?
  9. 9.Is 187500 divisible by 30?
  10. 10.Is 3676 divisible by 4?
  11. 11.Is 26014 divisible by 18?
  12. 12.Is 31572 divisible by 18?
  13. 13.Is 10397 divisible by 2?
  14. 14.Is 15752 divisible by 8?
  15. 15.Is 121209 divisible by 23?
  16. 16.Is 51460 divisible by 10?
  17. 17.Is 39520 divisible by 20?
  18. 18.Is 51252 divisible by 12?
  19. 19.Is 20973 divisible by 5?
  20. 20.Is 5702 divisible by 12?
  21. 21.Is 24250 divisible by 7?
  22. 22.Is 119628 divisible by 18?
  23. 23.Is 48981 divisible by 29?
  24. 24.Is 22218 divisible by 4?
  25. 25.Is 3120 divisible by 7?
  26. 26.Is 26740 divisible by 10?
  27. 27.Is 10304 divisible by 15?
  28. 28.Is 2371 divisible by 2?
  29. 29.Is 24526 divisible by 6?
  30. 30.Is 8202 divisible by 20?
  31. 31.Is 56727 divisible by 11?
  32. 32.Is 55810 divisible by 10?
  33. 33.Is 59490 divisible by 15?
  34. 34.Is 20943 divisible by 13?
  35. 35.Is 12044 divisible by 5?
  36. 36.Is 10258 divisible by 23?
  37. 37.Is 17010 divisible by 8?
  38. 38.Is 1470 divisible by 2?
  39. 39.Is 22526 divisible by 4?
  40. 40.Is 48475 divisible by 7?

Answer key

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

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