To determine if 3417 is prime, you would have to try dividing 3417 by every whole number less than 3416.
True or false
and how did you get the answer
Not true. Start with small prime numbers. You may find one that is an even divisor before you go through all numbers. Try 3, for example. You find right away that 3417 = 3 x 1139
So, 3417 is not prime.
You never have to go above N/2 as a divisor to prove that N is not prime. Numbers larger than N/2 cannot be integer factors
also apply the rules of divisibility
write the multiples of 2 up to 30
False.
To determine if a number is prime, you do not need to divide it by every whole number less than itself. That would be computationally inefficient and time-consuming.
The most efficient way to determine if a number is prime is to use a process called trial division. In trial division, you only need to divide the number by prime numbers up to the square root of that number.
To determine if 3417 is prime:
1. Find the square root of 3417. The square root of 3417 is approximately 58.43 (rounded to two decimal places).
2. Then, you would divide 3417 by prime numbers starting from 2 up to the square root of 3417 (rounded up), which is 59 in this case.
3. If none of the prime divisors evenly divide the number, then the number is prime. Otherwise, if any of them divide the number without leaving a remainder, then the number is composite.
In this case, you would need to divide 3417 by the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, and 59. If none of these primes divides 3417 without a remainder, then 3417 is prime.