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

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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