Question

Using Euclid’s division algorithm, find which of the following pairs of numbers

are coprimes.

(i) 255, 867 (ii) 615, 154 (iii) 847, 2160​

Answer 1

Answer:

ʜᴇʀᴇ ᴜs ʏᴏᴜʀ ᴀɴsᴡᴇʀ ⬇️

Step-by-step explanation:

ɢɪᴠᴇɴ, ᴛʜᴇ ᴛᴡᴏ ɴᴜᴍʙᴇʀs 847,2160

ʜᴇʀᴇ, ᴄᴏ-ᴘʀɪᴍᴇs ᴀʀᴇ 2 ɴᴜᴍʙᴇʀs ᴡʜɪᴄʜ ʜᴀᴠᴇ ᴏɴʟʏ ᴏɴᴇ ᴀs ᴀ ᴄᴏᴍᴍᴏɴ ғᴀᴄᴛᴏʀ.

ʟᴇᴛ, ᴀ=2160

ʙ=847

ᴛʜᴇɴ, ʙʏ ᴇᴜᴄʟɪᴅ's ʟᴇᴍᴍᴀ

ᴀ=ʙǫ+ʀ,0≤ʀ<ʙ

sᴏ,

2160=847×2+466

847=466×1+381

466=381×1+85

381=85×4+41

85=41×2+3

41=3×13+2

3=2×1+1

2=1×2+0

ᴀs 1 ɪs ᴛʜᴇ ʜ.ᴄ.ғ ᴏғ 847 ᴀɴᴅ 2160,

∴ 847 ᴀɴᴅ 2160 ᴀʀᴇ ᴄᴏ-ᴘʀɪᴍᴇs ᴀs ᴛʜᴇʏ ʜᴀᴠᴇ ᴏɴʟʏ 1 ᴀs ᴛʜᴇɪʀ ʜ.ᴄ.ғ.