determinate the smallest integer which has 28 divisors.


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Question Number 124512 by mathocean1 last updated on 03/Dec/20

$d e t e r m i n a t e t h e s m a l l e s t i n t e g e r$ $w h i c h h a s 28 d i v i s o r s .$
Commented by mr W last updated on 04/Dec/20

$960 ?$
Commented by mathocean1 last updated on 04/Dec/20

$p l e a s e s i r c a n y o u d e t a i l$
Commented by mr W last updated on 04/Dec/20

$n = p^{a} q^{b} r^{c} . . .$ $w i t h p, q, r, . . . = p r i m e = 2, 3, 5, . . .$ $(a + 1) (b + 1) (c + 1) . . . = 28 = 7 \times 4 = 7 \times 2 \times 2$ $c a s e 1 : a = 6, b = 3$ $n_{m i n} = 2^{6} 3^{3} = 1728$ $c a s e 2 : a = 6, b = 1, c = 1$ $n_{m i n} = 2^{6} 3^{1} 5^{1} = 960$ $\Rightarrow n_{m i n} = 960$
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