To determne whethr 617 is a prime #,it suffices to check tht no prime# less than __ is a factor of it.Explain.

Question

I am completely STUMPED.
Can anyone explain this?
"To determine whether 617 is a prime number, it suffices to check that no prime number less than ___ is a factor of it. Explain your answer."

Answer 1

The answer is sqrt(617) as you have probably gathered from all the other answers aready. But why is this true?

If you have two numbers greater than sqrt(617) and multiply them together, the product would be greater than 617. In looking for factors of 617, you only need to check all primes less than or equal to sqrt(617) since any number greater than sqrt(617) would have to be paired with a number less than sqrt(617) which you would have already checked.

Let's try it:
sqrt(617) = 24.8 approx
All primes less than 25 = 2, 3, 5, 7, 11, 13, 17, 19, 23

2 is obviously not a factor of 617 since 617 is not even.
617 / 3 = 205.67 approx, so 3 is not a factor
5 is obviously not a factor of 617, since 617 does not end in 0 or 5.
617 / 7 = 88.1 approx, so 7 is not a factor of 617.
617 / 11 = 56.1 approx, so 11 is not a factor of 617.
617 / 13 = 47.46 approx, so 13 is not a factor of 617.
617 / 17 = 36.3 approx, so 17 is not a factor of 617.
617 / 19 = 32.47 approx, so 19 is not a factor of 617.
617 / 23 = 26.82 approx, so 23 is not a factor of 617

Now look what happens when we continue this trend.
The next prime number would be 29.
617 / 29 = 21.27 approx, so 29 is not a factor of 617. But notice that 617/29 is less than the sqrt(617) and any factor you might find must have another factor less than sqrt(617) which we have already proven does not exist.

Is that good?

Answer 2

Your question is about prime numbers.

What is a prime number?

A prime number is a number that has exactly TWO factors and that can only be divided evenly (without a remainder) by 1 and ITSELF.

Your question can be written this way for easy reading:

To find if 617 is a prime number, it is enough to check that no prime number less than______is a factor of 617.

There is a missing number that you must place on the line to complete the given statement.

Can you take it from here?

Guido

Answer 3

list all the prime numbers less than 617 and see if any of these is a factor of 617.if none of these is a factor of 617,then 617 is a prime number.you maystart with 2 and then go on with 3,5,7,11,13 and so on

Answer 4

The guy at the top is correct. Take 64 for example. While checking only up to 32 would work, checking only up to 8 works as well, too; because every factor of 64 that is less than 8 must be multiplied by a number greater than 8 to equal 64.

Answer 5

You don't need to check any for any factors larger than the square root of the number being checked. A prime factor larger than the square root must have been multiplied by a prime factor smaller than the square root.

Answer 6

617 is correct

617 / 2 = 308.5 is also correct because the numbers between 308.5 and 617 are not factors in 617.

So you need to check from 308 and downwards.

Answer 7

Than the square root of 617 - about 24.8.

If you don't find any factors less than the square root, you won't find one greater than the square root (since you'd need to be able to pair it with one less than the square root).

Answer 8

squareroot(617)