Find the least number with 32 factors and at most 3 prime factors? Options: A . &nbsp 1920 B . &nbsp 2 7 3 3 C . &nbsp 1080 D . &nbsp 582 E . &nbsp none of these

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

Question

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

Answer: Option C
:
C

option (c)

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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