Find the least number with 32 factors and at most 3 prime factors?

1920

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2⁷3³

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1080

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none of these

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Solution

The correct option is C 1080
Let the prime factors be abc.

Ways of writing -

$a^{31}$ least value $= 2^{31}$

$a b^{15}$ least value $= 2^{15} 3$

$a^{3} b^{7}$ least value $= 2^{7} 3^{3}$

$a b^{3} c^{3}$ least value $= 2^{3} 3^{3} 5 = 1080$

$a b^{7} c$ least value $= 2^{7} 3^{1} 5^{1} = 1920$

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Find the least number with 32 factors and at most 3 prime factors?

The correct option is C 1080Let the prime factors be abc. Ways of writing - a31 least value =231 ab15 least value =2153 a3b7 least value =2733 ab3c3 least value =23335=1080 ab7c least value =273151=1920

The correct option is C 1080
Let the prime factors be abc.

Ways of writing -

$a^{31}$ least value $= 2^{31}$

$a b^{15}$ least value $= 2^{15} 3$

$a^{3} b^{7}$ least value $= 2^{7} 3^{3}$

$a b^{3} c^{3}$ least value $= 2^{3} 3^{3} 5 = 1080$

$a b^{7} c$ least value $= 2^{7} 3^{1} 5^{1} = 1920$