Question

Exᴘʟᴀɪɴ ᴡʜʏ 7×11×13+13 ᴀɴᴅ 7×6×5×4×3×2×1+5 ᴀʀᴇ ᴄᴏᴍᴘᴏsɪᴛᴇ ɴᴜᴍʙᴇʀs

Answer 1

${\underline{\underline{\frak{\purple{\dag\;AnswEr:-}}}}}$

$\underline {\rule{261}{2}}$

$\star\;{\underline{\underline{\sf{\pink{Composite\;number:}}}}}$

ᴀ ᴄᴏᴍᴘᴏsɪᴛᴇ ɴᴜᴍʙᴇʀ ɪs ᴀ ᴘᴏsɪᴛɪᴠᴇ ɪɴᴛᴇɢᴇʀ ᴛʜᴀᴛ ʜᴀs ᴀ ғᴀᴄᴛᴏʀ ᴏᴛʜᴇʀ ᴛʜᴀɴ 1 ᴀɴᴅ ɪᴛsᴇʟғ.

ɴᴏᴡ ᴄᴏɴsɪᴅᴇʀɪɴɢ ᴏᴜʀ ɴᴜᴍʙᴇʀ,

7 × 11 × 13 × 13 ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀs, 13[(7 × 11) + 1] ɪ.ᴇ. 13 × 78. sᴏ, ᴏᴛʜᴇʀ ᴛʜᴀɴ 1 ᴀɴᴅ ᴛʜᴇ ɴᴜᴍʙᴇʀ ɪᴛsᴇʟғ, 13 ᴀɴᴅ 78 ᴀʀᴇ ᴀʟsᴏ ᴛʜᴇ ғᴀᴄᴛᴏʀ ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀ.

ғᴜʀᴛʜᴇʀ, 78 = 39 × 2. sᴏ, 39 ᴀɴᴅ 2 ᴀʀᴇ ᴀʟsᴏ ɪᴛ's ғᴀᴄᴛᴏʀs. sᴏ, ᴛʜɪs ɴᴜᴍʙᴇʀ ɪs ᴅᴇғɪɴᴀᴛᴇʟʏ ɴᴏᴛ ᴘʀɪᴍᴇ. ʜᴇɴᴄᴇ, ɪᴛ ɪs ᴄᴏᴍᴘᴏsɪᴛᴇ ɴᴜᴍʙᴇʀ.

sɪᴍɪʟᴀʀʟʏ, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀs 5[(7 × 6 × 4 × 3 × 2 × 1) + 1] ɪ.ᴇ. 5 × 1009.

sᴏ, ᴏᴛʜᴇʀ ᴛʜᴀɴ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴀɴᴅ 1, ɪᴛ ʜᴀᴠᴇ 5 ᴀɴᴅ 1009 ᴀs ɪᴛ's ғᴀᴄᴛᴏʀ ᴛᴏᴏ. ʜᴇɴᴄᴇ, ɪᴛ ɪs ᴀʟsᴏ ᴀ ᴄᴏᴍᴘᴏsɪᴛᴇ ɴᴜᴍʙᴇʀ.

$\underline {\rule{261}{2}}$