ໃຊ້ວິທີ Euclidean ເພື່ອຫາ gcd ⁡ ( 758 , 242 )

👏👏ແກ້ບົດເຝິກຫັດມ.7ບົດທີ1

1️⃣ ຂັ້ນຕອນ 1: ໃຊ້ວິທີ Euclidean ເພື່ອຫາ $\gcd(758, 242)$

ຫາເສດຈາກການຫານ:

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2️⃣ ຂັ້ນຕອນ 2: ແທນກັບເພື່ອຫາຄ່າ $x, y$

ເລີ່ມຈາກສົມການສຸດທ້າຍ:

ຈາກ (5):

$$2 = 14 - 4 \times 3$$

ຈາກ (4): $4 = 18 - 14$ ແທນເຂົ້າໄປ:

$$2 = 14 - (18 - 14)\times 3$$ $$2 = 14 - [18 - 14]\times 3$$ $$2 = 14 - 3(18 - 14)$$ $$2 = 14 - 3(18) + 3(14)$$ $$2 = 14 + 3(14) - 3(18)$$ $$2 = 4(14) - 3(18)$$

ຈາກ (3): $14 = 32 - 18$

$$2 = 4(32 - 18) - 3(18)$$ $$2 = 4(32) - 4(18) - 3(18)$$ $$2 = 128 - 4(18) - 3(18)$$ $$2 = 128 - 7(18)$$ $$2 = 128 - 126$$ $$2 = 2$$

ຈາກ (2): $18 = 242 - 32 \times 7$

$$2 = 128 - 7[242 - 32 \times 7]$$ $$2 = 128 - 7(242) + 49(32)$$ $$2 = 128 - 1694 + 1568$$ $$2 = 2$$

ຈາກ (1): $32 = 758 - 242 \times 3$

$$2 = 49[758 - 242 \times 3] - 7(242)$$ $$2 = 49(758) - 147(242) - 7(242)$$ $$2 = 49(758) - 154(242)$$

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3️⃣ ສະຫຼຸບຄຳຕອບ:

$$\gcd(758, 242) = 758(49) + 242(-154)$$

ດັ່ງນັ້ນ:

• $x = 49$
• $y = -154$

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💡 ຄຳຕອບສຸດທ້າຍ:

$$\gcd (758,242)=2=758(49)+242(-154)$$

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