Factors of 313: Prime Factorization, Methods, and Examples

The factors of 313 are the numbers that are divided by 313 fully. The number 313 is a prime number with only two factors. The factors can be positive and negative. 

Factors Of 313

In this lesson, we will learn about the factors of 313.

Factors of 313

Here are the factors of number 313.

Factors of 313: 1, 313

Negative Factors of 313

The negative factors of 313 are similar to its positive aspects, just with a negative sign.

Negative Factors of 313: -1, -313

Prime Factorization of 313

The prime factorization of 313 is the way of expressing its prime factors in the product form.

Prime Factorization: 1 x 313

In this article, we will learn about the factors of 313 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 313?

The factors of 313 are 1 and 313. These numbers are the factors as they do not leave any remainder when divided by 313.

The factors of 313 are classified as prime numbers and composite numbers. The prime factors of the number 313 can be determined using the prime factorization technique.

How To Find the Factors of 313?

You can find the factors of 313 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 313, create a list containing the numbers that are exactly divisible by 313 with zero remainders. One important thing to note is that 1 and 313 are 313’s factors, as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 313 are determined as follows:

\[\dfrac{313}{1} = 313\]

Therefore, 1 and 313 are the factors of 313.

Total Number of Factors of 313

For 313, there are two positive factors and two negative ones. So in total, there are four factors of 313. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the factorization/prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure, the total number of factors of X is given as:

Factorization of 313 is 1 x 313.

The exponent of 1 and 313 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 313 is four. Two are positive, and two factors are negative.

Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

  • The factor of any given number must be a whole number.
  • The factors of the number cannot be in the form of decimals or fractions.
  • Factors can be positive as well as negative.
  • Negative factors are the additive inverse of the positive factors of a given number.
  • The factor of a number cannot be greater than that number.
  • Every even number has 2 as its prime factor, the smallest prime factor.

Factors of 313 by Prime Factorization

The number 313 is a prime number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors.prime factorization of 313

Before finding the factors of 313 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 313, start dividing by its most minor prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 313 can be expressed as:

313 = 1 x 313

Factors of 313 in Pairs

The factor pairs are the duplet of numbers that, when multiplied together, result in the factorized number. Factor pairs can be more than one depending on the total number of factors given.Factors of 313 in Pairs

For 313, the factor pairs can be found as:

1 x 313 = 313

The possible factor pairs of 313 are given as (1, 313).

All these numbers in pairs, when multiplied, give 313 as the product.

The negative factor pairs of 313 are given as:

-1 x -313 = 313 

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign, due to which the resulting product is the original positive number. Therefore, -1 and -313 are called negative factors of 313.

The list of all the factors of 313, including positive as well as negative numbers, is given below.

Factor list of 313: 1, -1, 313, and -313

Factors of 313 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 313 are there?


The total number of Factors of 313 is two.

Factors of 313 are 1 and 313.

Example 2

Find the factors of 313 using prime factorization.


The prime factorization of 313 is given as:

313 $\div$ 313 = 1 

So the prime factorization of 313 can be written as:

1 x 313 = 313

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