banner

Factors of 116: Prime Factorization, Methods, and Examples

The factors of 116 are the numbers that produce zero as a remainder when they act as a divisor for 116. Not only do these numbers produce a zero remainder, but they also yield a whole number quotient. 

The factors of 116 include all these numbers and their whole number quotients. These factors can be determined by the division method as well as the prime factorization methods. 

Factors of 116

Here are the factors of number 116.

Factors of 116: 1, 2, 4, 29, 58, 116

Negative Factors of 116

The negative factors of 116 are similar to its positive factors, just with a negative sign.

Negative Factors of 116: -1, -2, -4, -29, -58, and -116

Prime Factorization of 116

The prime factorization of 116 is the product of its prime factors.

Prime Factorization: 2 x 2 x 29

In this article, we will learn about the factors of 116 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 116?

The factors of 116 are 1, 2, 4, 29, 58, and 116. All of these numbers are the factors as they do not leave any remainder when divided by 116.

The factors of 116 are classified as prime numbers and composite numbers. The prime factors of the number 116 can be determined using the technique of prime factorization.

How To Find the Factors of 116?

You can find the factors of 116 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 116, create a list containing the numbers that are exactly divisible by 116 with zero remainders. One important thing to note is that 1 and 116 are the 116’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 116 are determined as follows:

\[\dfrac{116}{1} = 116\]

\[\dfrac{116}{2} = 58\]

\[\dfrac{116}{4} = 29\]

\[\dfrac{116}{29} = 4\]

\[ \dfrac{116}{58} = 2 \]

\[ \dfrac{116}{116} = 1\]

Therefore, 1, 2, 4, 29, 58, and 116 are the factors of 116.

Total Number of Factors of 116

For 116 there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 116. 

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 116 is given as:

Factorization of 116 is 1 x 2$^2$ x 29.

The exponent of 1 and 29 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 116 is 12, where 6 are positive factors and 6 are negative factors.

Important Notes

Here are some important 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 which is the smallest prime factor.

Factors of 116 by Prime Factorization

The number 116 is composite. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.

Before finding the factors of 116 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 116, start dividing by its smallest 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 116 can be expressed as:

116 = 2 x 2 x 29

Factors of 116 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

For 116, the factor pairs can be found as:

1 x 116 = 116 

2 x 58 = 116

4 x 29 =116 

The possible factor pairs of 116 are given as (1, 116), (2, 58), and (4, 29).

All these numbers in pairs, when multiplied, give 116 as the product.

The negative factor pairs of 116 are given as:

-1 x -116 = 116

-2 x -58 = 116 

-4 x -29 = 116

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, -29, -52, and -116 are called negative factors of 116.

The list of all the factors of 116 including positive as well as negative numbers is given as:

Factor list of 116 = 1, -1, 2, -2, 4, -4, 29, -29, 58, -58, 116, and -116.

Factors of 116 Solved Examples

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

Example 1

How many factors of 116 are there?

Solution

The total number of Factors of 116 is 6.

Factors of 116 are 1, 2, 4, 29, 58, and 116.

Example 2

Find the factors of 116 using prime factorization.

Solution

The prime factorization of 116 is given as:

116 $\div$ 2 = 58

58 $\div$ 2 = 29

29 $\div$ 29 =1 

So the prime factorization of 116 can be written as:

2 x 2 x 29 = 116

Factors of 115|Factors List| Factors of 117

5/5 - (6 votes)