Extrapolate these data

Number Theory Level 1

The sum of all the positive divisors of 2 is 3.
The sum of all the positive divisors of 3 is 4.
The sum of all the positive divisors of 4 is 7.
The sum of all the positive divisors of 5 is _ .

What is true about the number that goes in the blank?

It is greater than 7 It is equal to 7 It is less than 7

2 solutions

Michael Huang
Nov 28, 2016

For any prime number $p$ , since it contains only $p$ and $1$ as the divisors, the sum of the divisors must be $p + 1$ . Thus, since $5$ is prime, we have $5 + 1 = \boxed{6}$ , which is less than 7.

I think in this problem,that it is not said to extrapolate the pattern of the data:)

Anandmay Patel - 4 years, 6 months ago

Just to show how numbers work. I love working with patterns. :)

Michael Huang - 4 years, 6 months ago

Even i love to work with patterns :-)

Anandmay Patel - 4 years, 6 months ago

Munem Shahriar
Nov 26, 2017

5 is a prime number. That means it has only 2 divisors. Which is 1 and itself

Hence sum of all the positive divisors of 5 is $1 + 5 = 6$ . Which is less than 7

Extrapolate these data

2 solutions

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