what is the smallest natural number which has at least 100 divisors?


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Question Number 200236 by mr W last updated on 16/Nov/23

$w h a t i s t h e s m a l l e s t n a t u r a l n u m b e r$ $w h i c h h a s a t l e a s t 100 d i v i s o r s ?$
	Answered by MM42 last updated on 16/Nov/23

	$2^{4} \times 3^{4} \times 5 \times 7 = 45360 ✓$
	Commented by Rasheed.Sindhi last updated on 16/Nov/23

	$H o w t o p r o v e i t ?$
	Commented by MM42 last updated on 17/Nov/23

	$100 = 2 \times 2 \times 5 \times 5$ $n = 2^{a} \times 3^{b} \times 5^{c} \times 7^{d}$ $\Rightarrow D_{n} = (a + 1) (b + 1) (c + 1) (d + 1) = 100$ $w e g i v e t h e l a r g e s t p o w e r t o t h e$ $s m a l l e s t b a s e$
	Commented by Rasheed.Sindhi last updated on 16/Nov/23

	$T han k s sir!$
	Commented by mr W last updated on 17/Nov/23
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