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Factoring Practice, Study notes of Mathematics

Factoring Practice. I. Greatest Common Factor (GCF). Find the GCF of the numbers. 1. 12, 18. 2. 10, 35. 3. 8, 30. 4. 16, 24. 5. 28, 49. 6. 27, 63. 7. 30, 45.

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Factoring Practice
I. Greatest Common Factor (GCF)
Find the GCF of the numbers.
1. 12, 18
2. 10, 35
3. 8, 30
4. 16, 24
5. 28, 49
6. 27, 63
7. 30, 45
8. 48, 72
II. Greatest Common Monomial Factor
Factor, write prime if prime.
1. 6 3
2. 24
8
3. 6 12
4. 2
8
5. 4 10
6. 10
35
7. 10
15
8. 12
9 15
9. 3
12
30
10. 9
4 12
11. 2
3
5
12. 13 26
39
13. 17
34 51
14. 18
12
24
III. Factoring the Difference of Two Squares
Factor, write prime if prime.
1.
1
2.
9
3.
4
4.
25
5. 9
16
6. 4
25
7. 9
1
8.
9. 25
10.
16
11. 25
12.
16
13. 36
121
14. 2
8
15. 25 4
16. 4
81
17. 12
75
18.
19. 98 2
20. 5
45
21. 9
4
22. 16

·
·
 · ·
·
18, 30
6 = GCF
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Factoring Practice

I. Greatest Common Factor (GCF)

Find the GCF of the numbers.

II. Greatest Common Monomial Factor

Factor, write prime if prime.

2. 24ᡶ⡰^ ㎘ 8ᡶ

4. 2ᡶ⡰^ ㎗ 8ᡶ

6. 10ᡶ⡰^ ㎗ 35ᡶ

8. 12ᡶ⡰^ ㎘ 9ᡶ ㎗ 15

9. 3ᡦ⡱^ ㎘ 12ᡦ⡰^ ㎘ 30ᡦ

10. 9ᡥ⡰^ ㎘ 4ᡦ ㎗ 12

11. 2ᡶ⡱^ ㎘ 3ᡶ⡰^ ㎗ 5ᡶ

12. 13ᡥ ㎗ 26ᡥ⡰^ ㎘ 39ᡥ⡱

13. 17ᡶ⡰^ ㎗ 34ᡶ ㎗ 51

14. 18ᡥ⡰ᡦ⡲^ ㎘ 12ᡥ⡰ᡦ⡱^ ㎗ 24ᡥ⡰ᡦ⡰

III. Factoring the Difference of Two Squares

Factor, write prime if prime.

  1. ᡶ⡰^ ㎘ 1
  2. ᡶ⡰^ ㎘ 9
  3. ᡶ⡰^ ㎗ 4
  4. ᡶ⡰^ ㎘ 25
  5. 9ᡷ⡰^ ㎘ 16
  6. 4ᡶ⡰^ ㎘ 25
  7. 9ᡶ⡰^ ㎘ 1
  8. ᡓ⡰^ ㎘ ᡶ⡰
  9. 25 ㎘ ᡥ⡰
  10. ᡶ⡰^ ㎘ 16ᡷ⡰
  11. 25ᡥ⡰^ ㎘ ᡦ⡰

12. – ᡶ⡰^ ㎗ 16

13. 36ᡥ⡰^ ㎘ 121

14. 2ᡶ⡰^ ㎘ 8

16. 4ᡓ⡰^ ㎘ 81ᡔ⡰

17. 12ᡶ⡰^ ㎘ 75

20. 5ᡶ⡰^ ㎘ 45ᡷ⡰

21. 9ᡶ⡲^ ㎘ 4

22. 16ᡶ⡲^ ㎘ ᡷ⡰

❸➅ 㐄 ❹ · ➀ · ➀ ➀❷ 㐄 ❹ · ➀ · ➂ ❹ · ➀ 㐄 ➃

18, 30

6 = GCF

❸❹᠁➀᠂ ㎗ ❸➂᠁᠂➀^ 㐄 ➀᠁᠂㐵➁᠁❹^ ㎗ ➂᠂❹㐹

᠁❹^ ㎘ ➀➃ 㐄 䙦᠁ ㎗ ➃䙧䙦᠁ ㎘ ➃䙧

➀ᠤ❹^ ㎘ ➁➅ 㐄 ➀㐵ᠤ❹^ ㎘ ❸➃㐹 㐄 ➀䙦ᠤ ㎗ ➁䙧䙦ᠤ ㎘ ➁䙧

IV. Factoring Perfect Square Trinomials

Factor, write prime if prime.

  1. ᡶ⡰^ ㎗ 8ᡶ ㎗ 16
  2. ᡶ⡰^ ㎘ 16ᡶ ㎗ 64
  3. ᡷ⡰^ ㎗ 12ᡷ ㎗ 36
  4. ᡓ⡰^ ㎘ 10ᡓ ㎗ 25
  5. 16ᡷ⡰^ ㎗ 8ᡷ ㎗ 1

6. 9ᡶ⡰^ ㎘ 6ᡶ ㎗ 1

7. 25ᡶ⡰^ ㎗ 10ᡶ ㎗ 1

8. ᡦ⡰^ ㎘ 14ᡦ ㎗ 49

9. 81ᡶ⡰^ ㎘ 90ᡶ ㎗ 25

10. 4ᡷ⡰^ ㎘ 20ᡷ ㎗ 25

11. 25ᡓ⡰^ ㎗ 60ᡓ ㎗ 36

13. 16ᡶ⡰^ ㎗ 24ᡶ ㎗ 9

14. 49ᡶ⡰^ ㎘ 14ᡶ ㎗ 1

15. 9ᡷ⡰^ ㎘ 30ᡷ ㎗ 25

16. ᡦ⡰^ ㎗ 2ᡦ ㎗ 4

17. ᡔ⡰^ ㎗ 2ᡔ ㎗ 1

18. 36ᡶ⡰^ ㎗ 84ᡶ ㎗ 49

V. Special Factoring – Challenge

Factor, write prime if prime.

  1. ᡓ⡰^ ㎘ 36
  2. 9ᡶ⡰^ ㎘ 49
  3. 169ᡥ⡰^ ㎘ 4ᡳ⡰
  4. ᡶ⡰ᡷ⡰^ ㎘ 9ᡸ⡲
  5. ⡩⡲ ᡶ⡰^ ㎘ 25ᡷ⡰
  6. ⡩⡷ ᡶ⡰^ ㎘ 16
  7. 64 ㎘ ᡓ⡲ᡔ⡲
  8. ᡷ⡴^ ㎘ 100
  9. ⡲⡷ ᡶ⡰ᡷ⡰^ ㎘ ⡰⡳⡱⡴ ᡸ⡰
  10. ᡷ⡶^ ㎘ 81

12. ᡓ⡰ᡔ⡰^ ㎗ 6ᡓᡔ ㎗ 9

13. ᡶ⡰^ ㎗ 2ᡶᡷ ㎗ ᡷ⡰

14. 4ᡶ⡰^ ㎗ 12ᡶᡷ ㎗ 9ᡷ⡰

15. 100ᡠ⡰^ ㎗ 20ᡠ ㎗ 1

16. 9ᡓ⡰^ ㎘ 24ᡓ ㎗ 16

17. 4ᡓ⡱^ ㎗ 8ᡓ⡰^ ㎗ 4ᡓ

18. 5ᡕ ㎗ 20ᡕ⡰^ ㎗ 20ᡕ⡱

19. 䙦ᡶ ㎗ 4䙧⡰^ ㎘ 䙦ᡷ ㎗ 1䙧⡰

20. 䙦ᡶ ㎘ 1䙧⡰^ ㎘ 10䙦ᡶ ㎘ 1䙧 ㎗ 25

VI. Factoring Trinomials: x^2 + bx + c

Factor, write prime if prime.

  1. ᡶ⡰^ ㎗ 6ᡶ ㎗ 8
  2. ᡕ⡰^ ㎗ 5ᡕ ㎗ 6
  3. ᡷ⡰^ ㎘ 9ᡷ ㎗ 14
  4. ᡶ⡰^ ㎘ 10ᡶ ㎗ 16
  5. ᡓ⡰^ ㎗ 12ᡓ ㎗ 27
  6. ᡶ⡰^ ㎘ 14ᡶ ㎗ 24
  7. ᡶ⡰^ ㎘ 15ᡶ ㎗ 36
  8. ᡷ⡰^ ㎗ 21ᡷ ㎗ 54
  9. ᡥ⡰^ ㎗ 13ᡥ ㎘ 36
  10. ᡶ⡰^ ㎘ 8ᡶ ㎗ 15
  11. ᡷ⡰^ ㎘ 4ᡷ ㎘ 32

12. ᡶ⡰^ ㎘ ᡶ ㎘ 6

13. ᡷ⡰^ ㎗ 3ᡷ ㎘ 18

14. ᡔ⡰^ ㎗ 7ᡔ ㎘ 18

15. ᡓ⡰^ ㎗ ᡓ ㎘ 56

16. ᡕ⡰^ ㎘ 4ᡕ ㎘ 12

17. ᡶ⡰^ ㎘ 9ᡶ ㎘ 36

18. ᡷ⡰^ ㎗ 4ᡷ ㎘ 21

19. ᡶ⡰^ ㎘ 22ᡶ ㎘ 75

20. ᡶ⡰^ ㎘ 3ᡶ ㎘ 40

22. ᡶ⡰^ ㎘ 13ᡶ ㎗ 36

ᠤ❹^ ㎘ ❸➁ᠤ ㎗ ➁➆ 㐄 䙦ᠤ ㎘ ➄䙧❹

ᠤ❹^ ㎗ ➄ᠤ ㎗ ❸❷ 㐄 䙦ᠤ䙧❹^ ㎗ 䙦❹ ㎗ ➂䙧ᠤ ㎗ 䙦❹䙧䙦➂䙧 㐄 䙦ᠤ ㎗ ❹䙧䙦ᠤ ㎗ ➂䙧

X. Factoring: Putting It All Together

Factor Completely, write prime if prime.

  1. 2ᡶ⡰^ ㎘ 8
  2. 2ᡶ⡰^ ㎗ 8ᡶ ㎗ 6
  3. 3ᡦ⡰^ ㎗ 9ᡦ ㎘ 30
  4. 6ᡶ⡰^ ㎘ 26ᡶ ㎘ 20
  5. 2ᡶ⡰^ ㎗ 12ᡶ ㎘ 80
  6. 5ᡲ⡰^ ㎗ 15ᡲ ㎗ 10
  7. 8ᡦ⡰^ ㎘ 18
  8. 14ᡶ⡰^ ㎗ 7ᡶ ㎘ 21

9. 4ᡶ⡰^ ㎗ 16ᡶ ㎗ 16

10. 18ᡶ ㎗ 12ᡶ⡰^ ㎗ 2ᡶ⡱

12. 3ᡲ⡱^ ㎘ 27ᡲ

13. 24ᡓ⡰^ ㎘ 30ᡓ ㎗ 9

14. 10ᡶ⡰^ ㎗ 15ᡶ ㎘ 10

15. 3ᡶ⡰^ ㎘ 42ᡶ ㎗ 147

16. 4ᡶ⡲^ ㎘ 4ᡶ⡰

XI. …More Factoring: Putting It All Together

1. 16ᡶ⡰^ ㎘ 40ᡶ ㎘ 24

2. 27ᡶ⡰^ ㎘ 36ᡶ ㎗ 12

3. 5ᡶ⡰^ ㎘ 60ᡶ ㎘ 140

4. 6ᡥ⡱^ ㎗ 54ᡥ⡰^ ㎘ 6ᡥ

5. 5ᡣ⡲^ ㎗ 8ᡣ⡱^ ㎘ 4ᡣ⡰

6. ᡶ⡰ᡷ⡲^ ㎘ ᡶ⡴

7. ᡷ⡲^ ㎘ 6ᡷ⡰^ ㎘ 16

8. ᡶ⡲^ ㎘ 3ᡶ⡰^ ㎘ 4

9. ᡠ⡰^ ㎘ 䙦ᡓ⡰^ ㎘ 6ᡓ ㎗ 9䙧

10. 81ᡶ⡲^ ㎘ 16ᡷ⡲

11. 4ᡥᡦ⡰^ ㎘ 4ᡥ⡰ᡦ⡰^ ㎗ ᡥ⡱ᡦ⡰

12. 䙦2ᡓ ㎗ 3䙧⡰^ ㎘ 䙦ᡓ ㎘ 1䙧⡰

13. 16ᡖ⡶^ ㎘ 8ᡖ⡲^ ㎗ 1

14. ᡶ⡰䙦ᡶ⡰^ ㎘ 4䙧 ㎗ 4ᡶ䙦ᡶ⡰^ ㎘ 4䙧 ㎗ 4䙦ᡶ⡰^ ㎘ 4䙧

XII. Extra: Factoring by Grouping

1. ᡶ⡰^ ㎗ 2ᡶ ㎗ ᡶᡷ ㎗ 2ᡷ

2. 3ᡓ⡰^ ㎘ 2ᡔ ㎘ 6ᡓ ㎗ ᡓᡔ

  1. ᡲ⡱^ ㎘ ᡲ⡰^ ㎗ ᡲ ㎘ 1 Hint: ᡲ ㎘ 1 㐄 1䙦ᡲ ㎘ 1䙧
  2. 10 ㎗ 2ᡲ ㎘ 5ᡱ ㎘ ᡱᡲ
  3. ⡰⡱ ᡔᡕ ㎘ ⡩⡲⡱ ᡔ ㎗ ᡕ ㎘ 7
  4. 4ᡳ⡰^ ㎗ ᡴ ㎗ 2ᡳᡴ ㎗ 2ᡳ
  5. ᡓᡖ ㎗ 3ᡓ ㎘ ᡖ⡰^ ㎘ 3ᡖ

8. ᡦ⡰^ ㎗ 2ᡦ ㎗ 3ᡥᡦ ㎗ 6ᡥ

9. 2ᡓᡶ⡰^ ㎗ ᡔᡶ⡰^ ㎘ 2ᡓᡷ⡰^ ㎘ ᡔᡷ⡰

10. ᡷᡸ⡰^ ㎘ ᡷ⡱^ ㎗ ᡸ⡱^ ㎘ ᡷ⡰ᡸ

11. ᡷ⡱^ ㎘ ᡷ⡰^ ㎘ 4ᡷ ㎗ 4

13. ᡶ⡱^ ㎗ ᡶ⡰^ ㎘ ᡶ ㎘ 1

14. ᡓ⡱^ ㎘ ᡓ⡰^ ㎘ 8ᡓ ㎗ 8

➂ᠤ❹^ ㎗ ❹❷ᠤ ㎘ ➃❷ 㐄 ➂㐵ᠤ❹^ ㎗ ➁ᠤ ㎘ ❸❹㐹 㐄 ➂䙦ᠤ ㎗ ➃䙧䙦ᠤ ㎘ ❹䙧

㐄 ➀᠁䙦❹ᠤ ㎘ ❸䙧^ ㎗ ❹᠂䙦❹ᠤ ㎘ ❸䙧

Factoring Practice Key

I. Greatest Common Factor

  1. 6
  2. 5
  3. 2
  4. 8
  5. 7
  6. 9
  7. 15
  8. 24 II. Greatest Common Monomial Factor
  9. 3䙦2ᡶ ㎗ 1䙧
  10. 8ᡶ䙦3ᡶ ㎘ 1䙧
  11. 6䙦ᡶ ㎘ 2䙧
  12. 2ᡶ䙦ᡶ ㎗ 4䙧
  13. 2䙦2ᡶ ㎗ 5䙧
  14. 5ᡶ䙦2ᡶ ㎗ 7䙧
  15. 5ᡶᡷ䙦2ᡶ ㎘ 3ᡷ䙧
  16. 3䙦4ᡶ⡰^ ㎘ 3ᡶ ㎗ 5䙧
  17. 3ᡦ䙦ᡦ⡰^ ㎘ 4ᡦ ㎘ 10䙧
  18. prime
  19. ᡶ䙦2ᡶ⡰^ ㎘ 3ᡶ ㎗ 5䙧
  20. 13ᡥ䙦1 ㎗ 2ᡥ ㎘ 3ᡥ⡰䙧
  21. 17䙦ᡶ⡰^ ㎗ 2ᡶ ㎗ 3䙧
  22. 6ᡥ⡰ᡦ⡰䙦3ᡦ⡰^ ㎘ 2ᡦ ㎗ 4䙧 III. Factoring the Difference of Two Squares
  23. 䙦ᡶ ㎗ 1䙧䙦ᡶ ㎘ 1䙧
  24. 䙦ᡶ ㎗ 3䙧䙦ᡶ ㎘ 3䙧
  25. prime
  26. 䙦ᡶ ㎗ 5䙧䙦ᡶ ㎘ 5䙧
  27. 䙦3ᡷ ㎗ 4䙧䙦3ᡷ ㎘ 4䙧
  28. 䙦2ᡶ ㎗ 5䙧䙦2ᡶ ㎘ 5䙧
  29. 䙦3ᡶ ㎗ 1䙧䙦3ᡶ ㎘ 1䙧
  30. 䙦ᡓ ㎗ ᡶ䙧䙦ᡓ ㎘ ᡶ䙧
  31. 䙦5 ㎗ ᡥ䙧䙦5 ㎘ ᡥ䙧
  32. 䙦ᡶ ㎗ 4ᡷ䙧䙦ᡶ ㎘ 4ᡷ䙧
  33. 䙦5ᡥ ㎗ ᡦ䙧䙦5ᡥ ㎘ ᡦ䙧
  34. 䙦4 ㎗ ᡶ䙧䙦4 ㎘ ᡶ䙧
  35. 䙦6ᡥ ㎗ 11䙧䙦6ᡥ ㎘ 11䙧
  36. 2䙦ᡶ ㎗ 2䙧䙦ᡶ ㎘ 2䙧
  37. prime
  38. 䙦2ᡓ ㎗ 9ᡔ䙧䙦2ᡓ ㎘ 9ᡔ䙧
  39. 3䙦2ᡶ ㎗ 5䙧䙦2ᡶ ㎘ 5䙧
  40. ᡔ䙦ᡓ ㎗ ᡔ䙧䙦ᡓ ㎘ ᡔ䙧
  41. ㎘2䙦7 ㎗ ᡶ䙧䙦7 ㎘ ᡶ䙧 ᡧᡰ 2䙦ᡶ ㎗ 7䙧䙦ᡶ ㎘ 7䙧
  42. 5䙦ᡶ ㎗ 3ᡷ䙧䙦ᡶ ㎘ 3ᡷ䙧
  43. 䙦3ᡶ⡰^ ㎗ 2䙧䙦3ᡶ⡰^ ㎘ 2䙧
  44. 䙦4ᡶ⡰^ ㎗ ᡷ䙧䙦4ᡶ⡰^ ㎘ ᡷ䙧 IV. Factoring Perfect Square Trinomials
  45. 䙦ᡶ ㎗ 4䙧⡰
  46. 䙦ᡶ ㎘ 8䙧⡰
  47. 䙦ᡷ ㎗ 6䙧⡰
  48. 䙦ᡓ ㎘ 5䙧⡰
  49. 䙦4ᡷ ㎗ 1䙧⡰
  50. 䙦3ᡶ ㎘ 1䙧⡰
  51. 䙦5ᡶ ㎗ 1䙧⡰
  52. 䙦ᡦ ㎘ 7䙧⡰
  53. 䙦9ᡶ ㎘ 5䙧⡰
  54. 䙦2ᡷ ㎘ 5䙧⡰
  55. 䙦5ᡓ ㎗ 6䙧⡰
  56. 䙦4 ㎗ 5ᡶ䙧⡰
  57. 䙦4ᡶ ㎗ 3䙧⡰
  58. 䙦7ᡶ ㎘ 1䙧⡰
  59. 䙦3ᡷ ㎘ 5䙧⡰
  60. prime
  61. 䙦ᡔ ㎗ 1䙧⡰
  62. 䙦6ᡶ ㎗ 7䙧⡰
  63. 䙦ᡶ ㎘ 9䙧⡰
  64. 䙦3ᡷ ㎘ 2䙧⡰ V. Special Factoring – Challenge
  65. 䙦ᡓ ㎗ 6䙧䙦ᡓ ㎘ 6䙧
  66. 䙦3ᡶ ㎗ 7䙧䙦3ᡶ ㎘ 7䙧
  67. 䙦13ᡥ ㎗ 2ᡳ䙧䙦13ᡥ ㎘ 2ᡳ䙧
  68. 䙦ᡶᡷ ㎗ 3ᡸ⡰䙧䙦ᡶᡷ ㎘ 3ᡸ⡰䙧
  69. 䙲⡩⡰ ᡶ ㎗ 5ᡷ䙳 䙲⡩⡰ ᡶ ㎘ 5ᡷ䙳
  70. 䙲⡩⡱ ᡶ ㎗ 4䙳 䙲⡩⡱ ᡶ ㎘ 4䙳
  71. 䙦8 ㎗ ᡓ⡰ᡔ⡰䙧䙦8 ㎘ ᡓ⡰ᡔ⡰䙧
  72. 䙦ᡷ⡱^ ㎗ 10䙧䙦ᡷ⡱^ ㎘ 10䙧
  73. 䙲⡰⡱ ᡶᡷ ㎗ ⡳⡴ ᡸ䙳 䙲⡰⡱ ᡶᡷ ㎘ ⡳⡴ ᡸ䙳
  74. 䙦ᡷ⡲^ ㎗ 9䙧䙦ᡷ⡰^ ㎗ 3䙧䙦ᡷ⡰^ ㎘ 3䙧
  75. 䙦1 ㎘ 4ᡳ䙧⡰^ ᡧᡰ 䙦4ᡳ ㎘ 1䙧⡰
  76. 䙦ᡓᡔ ㎗ 3䙧⡰
  77. 䙦ᡶ ㎗ ᡷ䙧⡰
  78. 䙦2ᡶ ㎗ 3ᡷ䙧⡰
  79. 䙦10ᡠ ㎗ 1䙧⡰
  80. 䙦3ᡓ ㎘ 4䙧⡰
  81. 4ᡓ䙦ᡓ ㎗ 1䙧⡰
  82. 5ᡕ䙦2ᡕ ㎗ 1䙧⡰
  83. 䙰䙦ᡶ ㎗ 4䙧 ㎗ 䙦ᡷ ㎗ 1䙧䙱䙰䙦ᡶ ㎗ 4䙧 ㎘ 䙦ᡷ ㎗ 1䙧䙱 ᡧᡰ 䙦ᡶ ㎗ ᡷ ㎗ 5䙧䙦ᡶ ㎘ ᡷ ㎗ 3䙧
  84. 䙰䙦ᡶ ㎘ 1䙧 ㎘ 5䙱⡰^ ᡧᡰ 䙦ᡶ ㎘ 6䙧⡰ VI. Factoring Trinomials: x^2 + bx + c
  85. 䙦ᡶ ㎗ 4䙧䙦ᡶ ㎗ 2䙧
  86. 䙦ᡕ ㎗ 2䙧䙦ᡕ ㎗ 3䙧
  87. 䙦ᡷ ㎘ 7䙧䙦ᡷ ㎘ 2䙧
  88. 䙦ᡶ ㎘ 8䙧䙦ᡶ ㎘ 2䙧
  89. 䙦ᡓ ㎗ 9䙧䙦ᡓ ㎗ 3䙧
  90. 䙦ᡶ ㎘ 12䙧䙦ᡶ ㎘ 2䙧
  91. 䙦ᡶ ㎘ 12䙧䙦ᡶ ㎘ 3䙧
  92. 䙦ᡷ ㎗ 18䙧䙦ᡷ ㎗ 3䙧
  93. prime
  94. 䙦ᡶ ㎘ 5䙧䙦ᡶ ㎘ 3䙧
  95. 䙦ᡷ ㎘ 8䙧䙦ᡷ ㎗ 4䙧
  96. 䙦ᡶ ㎘ 3䙧䙦ᡶ ㎗ 2䙧
  97. 䙦ᡷ ㎗ 6䙧䙦ᡷ ㎘ 3䙧
  98. 䙦ᡔ ㎗ 9䙧䙦ᡔ ㎘ 2䙧
  99. 䙦ᡓ ㎗ 8䙧䙦ᡓ ㎘ 7䙧
  100. 䙦ᡕ ㎘ 6䙧䙦ᡕ ㎗ 2䙧
  101. 䙦ᡶ ㎘ 12䙧䙦ᡶ ㎗ 3䙧
  102. 䙦ᡷ ㎗ 7䙧䙦ᡷ ㎘ 3䙧
  103. 䙦ᡶ ㎘ 25䙧䙦ᡶ ㎗ 3䙧
  104. 䙦ᡶ ㎘ 8䙧䙦ᡶ ㎗ 5䙧