Math, asked by silentkiller000, 1 year ago

What is Euclidean Algorithm ? Explain.

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Answers

Answered by RAAJSRIWASTAV3

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♻Һ૯Ր૯ ɿς ע૦υՐ คՈςω૯Ր♻
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Aɴ ᴇғғɪᴄɪᴇɴᴛ ᴍᴇᴛʜᴏᴅ ғᴏʀ ᴄᴏᴍᴘᴜᴛɪɴɢ ᴛʜᴇ ɢʀᴇᴀᴛᴇꜱᴛ ᴄᴏᴍᴍᴏɴ ᴅɪᴠɪꜱᴏʀꜱ (GCD) ᴏғ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ, ᴛʜᴇ ʟᴀʀɢᴇꜱᴛ ɴᴜᴍʙᴇʀ ᴛʜᴀᴛ ᴅɪᴠɪᴅᴇꜱ ʙᴏᴛʜ ᴏғ ᴛʜᴇᴍ ᴡɪᴛʜᴏᴜᴛ ʟᴇᴀᴠɪɴɢ ᴀ ʀᴇᴍᴀɪɴᴅᴇʀ.

➡Iᴛ ɪꜱ ʙᴀꜱᴇᴅ ᴏɴ ᴛʜᴇ ᴘʀɪɴᴄɪᴘʟᴇ ᴛʜᴀᴛ ᴛʜᴇ ɢʀᴇᴀᴛᴇꜱᴛ ᴄᴏᴍᴍᴏɴ ᴅɪᴠɪꜱᴏʀ ᴏғ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ ᴅᴏᴇꜱ ɴᴏᴛ ᴄʜᴀɴɢᴇ ɪғ ᴛʜᴇ ʟᴀʀɢᴇʀ ɴᴜᴍʙᴇʀ ɪꜱ ʀᴇᴘʟᴀᴄᴇᴅ ʙʏ ɪᴛꜱ ᴅɪғғᴇʀᴇɴᴄᴇ ᴡɪᴛʜ ᴛʜᴇ ꜱᴍᴀʟʟᴇʀ ɴᴜᴍʙᴇʀ.

♦Eᴜᴄʟɪᴅᴇᴀɴ Aʟɢᴏʀɪᴛʜᴍ ɪꜱ ᴀʟꜱᴏ ᴋɴᴏᴡɴ ᴀꜱ "Eᴜᴄʟɪᴅ'ꜱ ᴀʟɢᴏʀɪᴛʜᴍ".

▶Fᴏʀ ᴇxᴀᴍᴘʟᴇ:-

21 ɪꜱ ᴛʜᴇ 'GCD' ᴏғ 252 & 105
(252 = 21 × 12 & 105 = 21 × 5),
& ᴛʜᴇ ꜱᴀᴍᴇ ɴᴜᴍʙᴇʀ 21 ɪꜱ ᴀʟꜱᴏ ᴛʜᴇ 'GCD' ᴏғ 105 & 252 − 105 = 147...

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