To find HCF of a given number by Experimental method
Answers
Answer:
ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ᴀʟɢᴏʀɪᴛʜᴍ ɪꜱ ᴀ ᴡᴀʏ ᴛᴏ ꜰɪɴᴅ ᴛʜᴇ ʜᴄꜰ ᴏꜰ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ ʙʏ ᴜꜱɪɴɢ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ. ɪᴛ ꜱᴛᴀᴛᴇꜱ ᴛʜᴀᴛ ɪꜰ ᴛʜᴇʀᴇ ᴀʀᴇ ᴀɴʏ ᴛᴡᴏ ɪɴᴛᴇɢᴇʀꜱ ᴀ ᴀɴᴅ ʙ, ᴛʜᴇʀᴇ ᴇxɪꜱᴛꜱ Q ᴀɴᴅ ʀ ꜱᴜᴄʜ ᴛʜᴀᴛ ɪᴛ ꜱᴀᴛɪꜱꜰɪᴇꜱ ᴛʜᴇ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ᴀ = ʙQ + ʀ ᴡʜᴇʀᴇ 0 ≤ ʀ < ʙ. ʟᴇᴛ'ꜱ ʟᴇᴀʀɴ ᴍᴏʀᴇ ᴀʙᴏᴜᴛ ɪᴛ ɪɴ ᴛʜɪꜱ ʟᴇꜱꜱᴏɴ.
ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ᴀʟɢᴏʀɪᴛʜᴍ
ᴀᴅᴅ
ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ᴀʟɢᴏʀɪᴛʜᴍ ɪꜱ ᴀ ᴡᴀʏ ᴛᴏ ꜰɪɴᴅ ᴛʜᴇ ʜᴄꜰ ᴏꜰ ᴛᴡᴏ ɴᴜᴍʙᴇʀꜱ ʙʏ ᴜꜱɪɴɢ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ. ɪᴛ ꜱᴛᴀᴛᴇꜱ ᴛʜᴀᴛ ɪꜰ ᴛʜᴇʀᴇ ᴀʀᴇ ᴀɴʏ ᴛᴡᴏ ɪɴᴛᴇɢᴇʀꜱ ᴀ ᴀɴᴅ ʙ, ᴛʜᴇʀᴇ ᴇxɪꜱᴛꜱ Q ᴀɴᴅ ʀ ꜱᴜᴄʜ ᴛʜᴀᴛ ɪᴛ ꜱᴀᴛɪꜱꜰɪᴇꜱ ᴛʜᴇ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ ᴀ = ʙQ + ʀ ᴡʜᴇʀᴇ 0 ≤ ʀ < ʙ. ʟᴇᴛ'ꜱ ʟᴇᴀʀɴ ᴍᴏʀᴇ ᴀʙᴏᴜᴛ ɪᴛ ɪɴ ᴛʜɪꜱ ʟᴇꜱꜱᴏɴ.
ᴡʜᴀᴛ ɪꜱ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ?
ᴇᴜᴄʟɪᴅ’ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ (ʟᴇᴍᴍᴀ ɪꜱ ʟɪᴋᴇ ᴀ ᴛʜᴇᴏʀᴇᴍ) ꜱᴀʏꜱ ᴛʜᴀᴛ ɢɪᴠᴇɴ ᴛᴡᴏ ᴘᴏꜱɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀꜱ ᴀ ᴀɴᴅ ʙ, ᴛʜᴇʀᴇ ᴇxɪꜱᴛ ᴜɴɪQᴜᴇ ɪɴᴛᴇɢᴇʀꜱ Q ᴀɴᴅ ʀ ꜱᴜᴄʜ ᴛʜᴀᴛ ᴀ = ʙQ + ʀ, 0≤ ʀ <ʙ. ᴛʜᴇ ɪɴᴛᴇɢᴇʀ Q ɪꜱ ᴛʜᴇ Qᴜᴏᴛɪᴇɴᴛ ᴀɴᴅ ᴛʜᴇ ɪɴᴛᴇɢᴇʀ ʀ ɪꜱ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ. ᴛʜᴇ Qᴜᴏᴛɪᴇɴᴛ ᴀɴᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ᴀʀᴇ ᴜɴɪQᴜᴇ.
ɪɴ ꜱɪᴍᴘʟᴇ ᴡᴏʀᴅꜱ, ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ ɪꜱ ᴡʜᴀᴛ ʏᴏᴜ ᴡᴇʀᴇ ᴜꜱɪɴɢ ᴛᴏ ᴄʜᴇᴄᴋ ᴛʜᴇ ᴀᴄᴄᴜʀᴀᴄʏ ᴏꜰ ᴅɪᴠɪꜱɪᴏɴ ɪɴ ʟᴏᴡᴇʀ ᴄʟᴀꜱꜱᴇꜱ, ᴡʜɪᴄʜ ɪꜱ ᴅɪᴠɪᴅᴇɴᴅ = ᴅɪᴠɪꜱᴏʀ × Qᴜᴏᴛɪᴇɴᴛ + ʀᴇᴍᴀɪɴᴅᴇʀ. ᴡʜᴇɴ ᴡᴇ ᴅɪᴠɪᴅᴇ ᴀ=39 ʙʏ ʙ=5, ᴡᴇ ɢᴇᴛ ᴛʜᴇ Qᴜᴏᴛɪᴇɴᴛ ᴀꜱ Q=7 ᴀɴᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ᴀꜱ ʀ=4. ʜᴇʀᴇ ɪꜱ ᴀɴ ᴇxᴀᴍᴘʟᴇ
Step-by-step explanation:
ᎻϴᏢᎬ ᎷᎽ ᎪΝՏᏔᎬᎡ ᏆՏ ᎻᎬᏞᏢҒႮᏞ ҒϴᎡ ᎽϴႮ (◕ᴗ◕✿)