Is 503 a Prime Number?

Yes, 503 is a prime number, because it is divisible by 1 and the number itself.
 

According to the definition of prime number, a prime number should have only two factors that are 1 and itself. As 503 meets the definition of prime number and it has only two factors that are 1 and 503. The following are the methods to be used to find whether 503 is a prime number or not. 

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

In this method, we will find out the number of divisors which can divide the given number evenly. Based on the count of divisors, we will categorize the number as either prime or composite.

If the count of divisors is 2 then the number is a prime number. 

If the count of divisors is more than 2 then the number is a composite number.

Step 1: Note that, not only 503 but also every number is divisible by 1

Step 2: Start dividing 503 by 2 and it cannot be divided by 2. So 2 is not a factor of 503.

Step 3: Then divide 503 by 3 and it cannot be divided by 3. So 3 is not a factor of 503.

Step 4: Likewise, we have to check up to the square root of 503.

√503= 22.42 (approximately)

Step 5: As we cannot find any divisors that can divide 503 evenly from 2 to 22.

Hence, 503 is a prime number as it has only two factors that are 1 and 503.
 

A divisibility test is a quick little trick used to find out if a number can be divided by another number. To find out if a number is divisible by any other number, we have to check all the numbers from 1 to the square root of the number.

Here, 503 is only divisible by 1 and 503. Hence, 503 is a prime number.

Since, the factors of 503 are 1 and 503.
 

Listing the prime numbers till 503: 2, 3, 5, 7, 11,13,17,19,23,29,31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 87, 89, 97, 101, 103, 107,109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,181, 191, 193, 197…… 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 503.

As 503 is present in the prime number chart, we can say that 503 is a prime number. 

Prime factorization is the method in which a number can be represented as a product of its prime factors. In this method we break down the number into its prime factors whose product will be obtaining the original number.

The prime factorization for 503 is 503  1.
 

• Prime numbers: Prime numbers are the numbers greater than 1 which are divisible by only 1 and itself. For example: 2,3,5…

• Factor: A number which can be multiplied with another number in order to obtain the required number. For example, 4 and 3 can be multiplied together to obtain 12. Hence 4 and 3 can be considered as factors of 12.

• Co-prime Numbers: The numbers which have only one common factor as 1. For example, 17 and 19 are co-primes because they have only one common factor which is 1.

• Multiple: A multiple of a number, such as 5, is obtained by multiplying it with any integer. For example, 5 × 1 = 5, 5 × 2 = 10.