One of these numbers is not like the others

Number Theory Level 2

We call a proper divisor of a positive integer to be a divisor of other than itself.

Which of the following numbers has the largest proper divisor?

47 67 57 37

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Munem Shahriar
Jan 25, 2018

Other than 57, all options are prime numbers. So they have only one proper divisor. Which is 1.

Since 57 ÷ 3 = 19 57 \div 3 = 19 and 19 > 1 , 57 19 > 1, \boxed{57} has the largest proper divisor.

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Anandmay Patel
Oct 14, 2016

I don't know whether the question is asking for the largest proper divisor or the largest number of proper divisors ,either way,the answer will be 57 .

As we can see that 57 is a semi-prime ,and all the rest are primes,it is obvious that 57 has the largest number of proper divisors.

On the other hand,again 57 has the largest proper divisor(19) among others(others has largest proper divisor as 1).

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