Question

How many 4 digit numbers have odd number of factors?

Answer 1

$1000, 1001, \cdot\cdot\cdot,9998,9999\:are\\Four \:digit \: numbers$

$\pink { Every\: perfect \: square \:has \:odd}$

$\pink { number \:of \: Factors. }$

$We \:know \:that ,$

• 31² = 961 ( 3 digit number )
• 32² = 1024 ( 4 digit first number which has odd number of factors)
• 99² = 9801 ( 4 digit last number which has odd number of factors )

$Number \:of \:4 \:digit \: numbers \: have \:odd\\number \: of \:factors\\ = 99 - 32 + 1 \\= 99 - 31 \\= 68$

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