Factors of 316: Prime Factorization, Methods, and Examples

The factors of 316 are the numbers upon which the number 316 is completely divisible. This means that these numbers give zero as the remainder and a whole number quotient as the product. 

Factors Of 316

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 316

Here are the factors of number 316.

Factors of 316: 1, 2, 4, 79, 158, 316

Negative Factors of 316

The negative factors of 316 are similar to its positive aspects, just with a negative sign.

Negative Factors of 316: -1, -2, -4, -79, -158, and -316

Prime Factorization of 316

The prime factorization of 316 is the way of expressing its prime factors in the product form.

Prime Factorization: $2^{2}$ x 79

In this article, we will learn about the factors of 316 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 316?

The factors of 316 are 1, 2, 4, 79, 158, and 316. These numbers are the factors as they do not leave any remainder when divided by 316.

The factors of 316 are classified as prime numbers and composite numbers. The prime factors of the number 316 can be determined using the prime factorization technique.

How To Find the Factors of 316?

You can find the factors of 316 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 316, create a list containing the numbers that are exactly divisible by 316 with zero remainders. One important thing to note is that 1 and 316 are the 316’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 316 are determined as follows:

\[\dfrac{316}{1} = 316\]

\[\dfrac{316}{2} = 158\]

\[\dfrac{316}{4} = 79\]

\[\dfrac{316}{316} = 1\]

Therefore, 1, 2, 4, and 316 along with the whole number quotients 79 and 158 are the factors of 316.

Total Number of Factors of 316

For 316, there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 316. 

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

  1. Find the 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 316 is given as:

Factorization of 316 is 1 x $2^{2}$ x 79.

The exponent of 1 and 79 is 1, and that of 2 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 316 is 12. 6 are positive, and 6 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 316 by Prime Factorization

The number 316 is a composite 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 316

Before finding the factors of 316 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 316, 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 316 can be expressed as:

316 = $2^{2}$ x 79

Factors of 316 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 316 in Pairs

For 316, the factor pairs can be found as:

1 x 316 = 316

2 x 158 = 316

4 x 79 = 316 

The possible factor pairs of 316 are given as (1, 316), (2, 158), and (4, 79).

All these numbers in pairs, when multiplied, give 316 as the product.

The negative factor pairs of 316 are given as:

-1 x -316 = 316

-2 x -158 = 316

-4 x -79 = 316 

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, -4, -79, -158 and -316 are called negative factors of 316.

The list of all the factors of 316, including positive as well as negative numbers, is given below.

Factor list of 316: 1, -1, 2, -2, 4, -4, 79, -79, 158, -158, 316, and -316

Factors of 316 Solved Examples

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

Example 1

How many factors of 316 are there?

Solution

The total number of Factors of 316 is 6.

Factors of 316 are 1, 2, 4, 79, 158, and 316.

Example 2

Find the factors of 316 using prime factorization.

Solution

The prime factorization of 316 is given as:

316 $\div$ 2 = 158 

158 $\div$ 2 = 79

79 $\div$ 79 = 1 

So the prime factorization of 316 can be written as:

$2^{2}$ x 79 = 316

Factors of 315|Factors List| Factors of 317