Is 313 a Prime Number?

A number to be identified as a prime number: the number should not have more than two factors, that too only 1 and itself, or else it is a composite number. 313 is a prime number, since factors of 313 are 1 and 313, where the count of factors is exactly two, hence, it is a prime number.

We will now check through various methods to see if 313 is a prime number or not. Let’s proceed.

• Counting Divisors Method

• Prime Number Chart

• Prime Factorization Method
   

The only condition this method involves is that a particular number is prime if and only if it has two distinct integers as its divisors. In the case of 313, the distinct divisors are: 1 and 313. Hence, there exist not more than two divisors of 313. Hence, 313 is prime.

The list of prime numbers up to 400 are →

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397

Following the above chart for reference, we can see that 313 is in the list. Hence, 313 is a prime number.
 

Prime factorization of, 313

313 = 1×313 

313 is not being easily factored into distinct smaller prime factors, clearly making it a prime number. 
 

• Cryptography: This is the branch which deals with cybersecurity, applying encoding-decoding methods.

• Prime Factorization: The process of breaking down a number into the product of its prime factors only, is called Prime Factorization. 

• Composite numbers: Composite numbers are numbers which have factors more than two.

• Twin prime numbers: Twin primes are those prime number pairs that have a difference of 2. 

• Perfect Divisor: Integers that divide into numbers, leaving no remainders behind. 

• Primality: The property of being a prime number, which is a natural number with factors only of itself and 1.