Question

Find the hcf of 50 and 26 by Euclid's Division lemma through an activity

Answer 1

Answer:

ʜᴄꜰ ᴏꜰ 26, 50 ʙʏ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱᴏɴ ʟᴇᴍᴍᴀ ᴍᴇᴛʜᴏᴅ ᴄᴀɴ ʙᴇ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ ᴇᴀꜱɪʟʏ ʙʏ ᴜꜱɪɴɢ ᴏᴜʀ ꜰʀᴇᴇ ᴏɴʟɪɴᴇ ʜᴄꜰ ᴜꜱɪɴɢ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱᴏɴ ʟᴇᴍᴍᴀ ᴄᴀʟᴄᴜʟᴀᴛᴏʀ ᴀɴᴅ ɢᴇᴛ ᴛʜᴇ ʀᴇꜱᴜʟᴛ ɪɴ ᴀ ꜰʀᴀᴄᴛɪᴏɴ ᴏꜰ ꜱᴇᴄᴏɴᴅꜱ ɪᴇ., 2 ᴛʜᴇ ʟᴀʀɢᴇꜱᴛ ꜰᴀᴄᴛᴏʀ ᴛʜᴀᴛ ᴇxᴀᴄᴛʟʏ ᴅɪᴠɪᴅᴇꜱ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ ᴡɪᴛʜ ʀ=0.

ʜɪɢʜᴇꜱᴛ ᴄᴏᴍᴍᴏɴ ꜰᴀᴄᴛᴏʀ (ʜᴄꜰ) ᴏꜰ 26, 50 ɪꜱ 2.

ʜᴄꜰ(26, 50) = 2

ᴇx: 10, 15, 20 (ᴏʀ) 24, 48, 96,45 (ᴏʀ) 78902, 89765, 12345

step by step:

ꜱᴛᴇᴘ 1: ꜱɪɴᴄᴇ 50 > 26, ᴡᴇ ᴀᴘᴘʟʏ ᴛʜᴇ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ ᴛᴏ 50 ᴀɴᴅ 26, ᴛᴏ ɢᴇᴛ

50 = 26 x 1 + 24

ꜱᴛᴇᴘ 2: ꜱɪɴᴄᴇ ᴛʜᴇ ʀᴇᴍɪɴᴅᴇʀ 26 ≠ 0, ᴡᴇ ᴀᴘᴘʟʏ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ ᴛᴏ 24 ᴀɴᴅ 26, ᴛᴏ ɢᴇᴛ

26 = 24 x 1 + 2

ꜱᴛᴇᴘ 3: ᴡᴇ ᴄᴏɴꜱɪᴅᴇʀ ᴛʜᴇ ɴᴇᴡ ᴅɪᴠɪꜱᴏʀ 24 ᴀɴᴅ ᴛʜᴇ ɴᴇᴡ ʀᴇᴍᴀɪɴᴅᴇʀ 2, ᴀɴᴅ ᴀᴘᴘʟʏ ᴛʜᴇ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ ᴛᴏ ɢᴇᴛ

24 = 2 x 12 + 0

ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ʜᴀꜱ ɴᴏᴡ ʙᴇᴄᴏᴍᴇ ᴢᴇʀᴏ, ꜱᴏ ᴏᴜʀ ᴘʀᴏᴄᴇᴅᴜʀᴇ ꜱᴛᴏᴘꜱ. ꜱɪɴᴄᴇ ᴛʜᴇ ᴅɪᴠɪꜱᴏʀ ᴀᴛ ᴛʜɪꜱ ꜱᴛᴀɢᴇ ɪꜱ 2, ᴛʜᴇ ʜᴄꜰ ᴏꜰ 26 ᴀɴᴅ 50 ɪꜱ 2

ɴᴏᴛɪᴄᴇ ᴛʜᴀᴛ 2 = ʜᴄꜰ(24,2) = ʜᴄꜰ(26,24) = ʜᴄꜰ(50,26) .

ᴛʜᴇʀᴇꜰᴏʀᴇ, ʜᴄꜰ ᴏꜰ 26,50 ᴜꜱɪɴɢ ᴇᴜᴄʟɪᴅ'ꜱ ᴅɪᴠɪꜱɪᴏɴ ʟᴇᴍᴍᴀ ɪꜱ 2.

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