Question

Hᴏʟᴀ!!!


ғɪɴᴅ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ ʙʏ ᴡʜɪᴄʜ 1575 ᴍᴜsᴛ ʙᴇ ᴅɪᴠɪᴅᴇᴅ ᴛᴏ ɢᴇᴛ ᴀ ᴘᴇʀғᴇᴄᴛ sǫᴜᴀʀᴇ.

ᴘʟᴇᴀsᴇ ᴀɴsᴡᴇʀ ᴛʜɪs ǫᴜᴇsᴛɪᴏɴ ᴏғ ᴄʟᴀss 8

Sᴘᴀᴍ= ɪᴅ ʀᴇᴘᴏʀᴛᴇᴅ
ɴᴇᴇᴅ ғᴜʟʟ sᴏʟᴜᴛɪᴏɴ​

Answer 1

$\large\mathbf{QUESTION}$

ғɪɴᴅ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ ʙʏ ᴡʜɪᴄʜ 1575 ᴍᴜsᴛ ʙᴇ ᴅɪᴠɪᴅᴇᴅ ᴛᴏ ɢᴇᴛ ᴀ ᴘᴇʀғᴇᴄᴛ sǫᴜᴀʀᴇ

$\huge\underline\bold\pink{Answer}$

Given number is 1575 first we write it as the product of prime factors

3 |1575

3 |525

5 | 175

5 | 35

7 | 7

__| 1

∴ 1575= 3×3 × 5×5 ×7

Clearly 7 has no pair so if we divide it by 7 then quotient become a perfect square.

${Your\: ans\: is\: 7}$

$\huge\mathfrak{\: \: \: \: \: \: hope \:that \:helps!!!}$

$\huge{\:\:\:\:\:\:\:✰CᴏᴢʏVɪʙᴇ✰}$

Answer 2

.

ғɪɴᴅ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ ɴᴜᴍʙᴇʀ ʙʏ ᴡʜɪᴄʜ 1575 ᴍᴜsᴛ ʙᴇ ᴅɪᴠɪᴅᴇᴅ ᴛᴏ ɢᴇᴛ ᴀ ᴘᴇʀғᴇᴄᴛ sǫᴜᴀʀᴇ

$\huge\underline\bold\pink{Answer}</p><p>$

$Given \: number \: is \: 1575 \: first \: we \: write \: it \: as \: the \: product \: of \: prime \: factors$

$3 |1575 </p><p></p><p> \\ 3 |525 \\ 5 |175 \\ 5 |35 \\ 7 |7 \\ 1$

$∴ 1575= 3×3 × 5×5 ×7$

$Clearly \: 7 \: has \: no \: pair \: so \: if \: we \: divide \: it \: by \: 7 \: then \: quotient \: become \: a \: perfect \: square.</p><p>$

so the answer is 7