Is 457 a prime number?
To determine whether 457 is a prime number, a guy investigates by testing the divisibility of smaller prime numbers. If he starts by checking the prime numbers 2, 3, 5, 7......, what is the last prime he needs to check before he can conclude that 457 is a prime number
Comments
The last prime that will need to be checked will be the largest one below the square root of the number.
If you divide 457 by a number greater than sqrt(457) you will get a number less than sqrt(457), so if the larger number divided into it exactly, so will the smaller. From this we see we only need to check up to the square root of the number.
21^2 = 441, and 22^2 = 484, so
sqrt(457) is between 21 and 22.
So we see we need the largest prime less than or equal to 21.
This prime is 19. So 19 is the last prime he needs to check.
If you do check the divisibility of 457 by all the primes up to 19 we find that none divide the number exactly, so 457 is prime.
The largest prime number less than or equal to the square root of 457 (approx 21.4). In this case 19 is the largest prime less than the square root.
the general test for the largest number to check is to take the square root of the number; if sqrt(n) or a number near sqrt(n) divides into n evenly, then the othe factor must be close in magnitude (or equal in magnitude) to sqrt(n)
sqrt(457)=21.38
the last integer you need to check is 21 (and 457 is a prime number)
19
23^23 = 529
I think u have to go to the nearest square root of that number only
e.g. for 457 calculate uptill 21 only........
Yes
no its not a prime no.
TRY TO DIVIDE IT WITH ALL NO. TILL ITS HALF NO. DONT COME
TRY IT.
Yes it is!
yes i think soo