A number theory problem by Benedict Dimacutac

Number Theory Level 4

Let $N$ be the smallest three-digit positive number with exactly 8 positive even divisors.

Then the sum of the digits of $N$ would be

12 9 13 4

2 solutions

Sergio La Malfa
Jul 21, 2018

Chan Lye Lee
Oct 30, 2017

$\cancel{N=2^8=256}$ . The sum of digits is $\cancel{2+5+6=13}$ .

The above is wrong, my bad... I did not think of it carefully! The correct answer should be $108=2^2\times 3$ , not $48=2^4\times 3$ , as the question requires for 3-digit positive number.

How do you know that $N$ must be equal to $2^8$ ?

Pi Han Goh - 3 years, 7 months ago

@Pi Han Goh , My mistake!

Chan Lye Lee - 3 years, 7 months ago

This is wrong. The answer is 2^4*3 = 48 .

Siva Budaraju - 3 years, 7 months ago

@Siva Budaraju Thanks for comment. However the question requires for 3-digit positive number.

Chan Lye Lee - 3 years, 7 months ago

A number theory problem by Benedict Dimacutac

2 solutions

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