Posted by **kim** on Wednesday, April 18, 2007 at 8:55pm.

Which of these is a prime number?

407, 409, 411, or 413

409

how did you get that?

Suppose you are given some number N. If x<sqrt[N] then N/x will be larger than sqrt[N]. This means that any factor of N must be smaller than or equal to the square root of N. This follows because if N has a factor larger than the square root of N 8other than N itself), then after dividing N by that number you would get a number smaller than the square root of N (that number is then not equal to 1). However, that number you get upon division will be a divisor of N too. That then contradicts the assumption that N has only divisors larger than the square root of N.

So, what you do is you check all the prime numbers till the square root of N to see if they divide N.

## Answer This Question

## Related Questions

- Math ? - Which of these numbers is prime? Explain why or why not. 407 409 411 ...
- math - The Florida Lottery is made up of the numbers 1-49. My mother has ...
- math - The Florida Lottery is made up of the numbers 1-49. My mother has ...
- Math - How do you find a square root of a number that's not a perfect square? I'...
- math - the florida lottery is made up of the number 1-49. my mother observed ...
- PROBLEM SOLVING IN MATHEMATICS - there are two prime numbers between 100 and 199...
- Math - A positive integer n is defined as a "prime interlude" if n-1 and n+1 are...
- Math - Which of the following is a prime #? a.2 b.19 c.37 d.51 e.67 I choose 2. ...
- Math Prime Numbers - Grade 7 question: I am a two-digit prime number I am one ...
- Math - The number p is the product of three different positive prime numbers ...

More Related Questions