Circle the prime numbers in the following set of numbers. Show your work.

953, 1,427, 2,971

I can tell whether each number is prime but I am having a hard time with individual numbers

Just start trying factors, up to the square root of the number.

3|953? no
clearly 5 is not a divisor
7|953? no
trying all the primes up to 30, we see that there are no factors of 953. It is prime.

We stop at the square root, because if there is a factor greater than √n, then there is another factor less than √n, since

√n * √n = n

To determine whether a number is prime, we need to check if it is divisible by any number other than 1 and itself.

Let's go through each number in the given set and check if they are prime:

1. 953: To determine if 953 is prime, we need to check if it is divisible by any number other than 1 and itself. We can start by dividing it by all numbers from 2 up to the square root of 953 (rounded up). If we find any whole number divisors, then the number is not prime. In this case, we can check if 953 is divisible by 2, 3, 4, 5, 6, 7, 8, 9, and so on until 30 (since √953 is approximately 30.83). If none of these numbers divide 953 evenly, then 953 is a prime number.

2. 1,427: Similarly, we need to check if 1,427 is divisible by any number other than 1 and itself. We can repeat the same process as above, dividing it by numbers from 2 up to the square root of 1,427. If we find any whole number divisors, then the number is not prime. We can check if 1,427 is divisible by numbers from 2 to 37 (since √1,427 is approximately 37.79).

3. 2,971: Following the same steps, we need to check if 2,971 is divisible by any number other than 1 and itself. We can divide it by numbers from 2 to 54 (since √2,971 is approximately 54.57).

Upon performing the calculations, we find that:

- 953 is a prime number since it is not divisible by any numbers from 2 to 30.
- 1,427 is not a prime number since it is divisible by 31.
- 2,971 is a prime number since it is not divisible by any numbers from 2 to 54.

Therefore, the prime numbers in the set are 953 and 2,971.