Is 437 a Prime Number?

We call a number prime only if it is divisible by 1 and itself. Taking the number 437, we know that 437 is divisible by 1 and itself. But it is also divisible by 19 and 23, so it is not a prime number.
 

A number is considered a non-prime if it has two or more factors. In the case of 437, there are four factors: 1, 19, 23, and 437. Let’s look at a few methods used for calculating prime numbers:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization 
    

If a number has only 2 divisors, then it is considered a prime number. This means that if there are more than two divisors, it would be considered a non-prime number. In the case of 437, we can see that there are more than two divisors. 

Step 1: Start with 1 and 437.

Step 2: Starting with 2, divide 437 until we get a whole remainder

437/2 = 218.5

437/3 = 145.667

until.…  

437/19 = 23

Step 3: Count the divisors

Here we see that we have 1, 19, 23, and 437 which totals to 4 divisors. Which means that 437 is not a prime number.
 

This method requires us to use the number to be checked (in this case, 437). When divided with the divisor, there should be no remainder for it to be a prime number.

Step 1: Start dividing with small numbers like 2 or 3.

Step 2: List the divisors that have a whole number as a remainder.

Step 3: Stop once you find all divisors. 

Here, 437 is divisible with numbers other than 1 and its own. Therefore, it’s a non-prime number.
 

The prime number chart is used to determine whether 437 is a prime number or not. We will use the range from 401 to 500 to see whether 437 is a prime number: 

401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 451, 463, 467, 479, 487, 491, 499. 

Here we see that 437 is not in the chart. This means that 437 is not a prime number. 
 

Prime factorization is a useful method used to break down composite numbers into their prime factors. So let's get into the prime factorization for the number 437. 

Step 1: We check by taking the lowest common factor, which is 2 

Step 2: Check to see if the number is divisible. 

437/19 = 23. 

Since 23 is a prime number, we can't divide it further. Therefore, we can conclude that 437 is a non-prime number and the factors are 1, 19, 23, and 437.
 

• GCF: The largest number that can be divided into 2 or more numbers without remainders.

• Remainders: A leftover number after dividing one number with another.

• Divisors: A number that can be divided by another number.