Factors of 310: Prime Factorization, Methods, and Examples

The factors of 310 are the numbers that can evenly divide 310 into equal parts. The number 310 is an even composite that shows that it has more than two factors. 

Factors Of 310

The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 310

Here are the factors of number 310.

Factors of 310: 1, 2, 5, 10, 31, 62, 155, 310

Negative Factors of 310

The negative factors of 310 are similar to its positive aspects, just with a negative sign.

Negative Factors of 310: -1, -2, -5, -10, -31, -62, -155, -310

Prime Factorization of 310

The prime factorization of 310 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 5 x 31

In this article, we will learn about the factors of 310 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 310?

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, and 310. These numbers are the factors as they do not leave any remainder when divided by 310.

The factors of 310 are classified as prime numbers and composite numbers. The prime factors of the number 310 can be determined using the prime factorization technique.

How To Find the Factors of 310?

You can find the factors of 310 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 310, create a list containing the numbers that are exactly divisible by 310 with zero remainders. One important thing to note is that 1 and 310 are 310’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 310 are determined as follows:

\[\dfrac{310}{1} = 310\]

\[\dfrac{310}{2} = 155\]

\[\dfrac{310}{5} = 62\]

\[\dfrac{310}{10} = 31\]

\[\dfrac{310}{310} = 1\]

Therefore, 1, 2, 5, 10, 31, 62, 155, and 310 are the factors of 310.

Total Number of Factors of 310

For 310, there are eight positive factors and eight negative ones. So in total, there are sixteen factors of 310. 

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 310 is given as:

Factorization of 310 is 1 x 2 x 5 x 31.

The exponent of 1, 2, 5, and 31 is 1.

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

Therefore, the total number of factors of 310 is 16. Eight are positive, and eight 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 310 by Prime Factorization

The number 310 is a composite. 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 310

Before finding the factors of 310 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 310, 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 310 can be expressed as:

310 = 2 x 5 x 31

Factors of 310 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 310 in Pairs

For 310, the factor pairs can be found as:

1 x 310 = 310

2 x 155 = 310 

5 x 62 = 310

10 x 31 = 310  

The possible factor pairs of 310 are given as (1, 310), (2, 155), (5, 62), and (10, 31).

All these numbers in pairs, when multiplied, give 310 as the product.

The negative factor pairs of 310 are given as:

-1 x -310 = 310

-2 x -155 = 310 

-5 x -62 = 310

-10 x -31 = 310  

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, -2, -5, -10, -31, -62, -155, and -310 are called negative factors of 310.

The list of all the factors of 310, including positive as well as negative numbers, is given below.

Factor list of 310: 1, 2, 5, 10, 31, 62, 155, 310, -1, -2, -5, -10, -31, -62, -155, and -310

Factors of 310 Solved Examples

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

Example 1

How many factors of 310 are there?

Solution

The total number of Factors of 310 is m.

Factors of 310 are 1, 2, 5, 10, 31, 62, 155,  and 310.

Example 2

Find the factors of 310 using prime factorization.

Solution

The prime factorization of 310 is given as:

310 $\div$ 2 = 155 

155 $\div$ 5 = 31 

31 $\div$ 31 = 1 

So the prime factorization of 310 can be written as:

2 x 5 x 31 = 310

Factors of 309|Factors List| Factors of 311