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Factors of 113: Prime Factorization, Methods, and Examples

The factors of 113 are numbers in pairs when multiplied together resulting in 113. The factors of any number can be explained as the numbers that are completely divisible by that particular number. This means the numbers that completely divided the given number are named as its factors.

The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 113

Here are the factors of number 113.

Factors of 113: 1, 113

Negative Factors of 113

The negative factors of 113 are similar to its positive factors, just with a negative sign.

Negative Factors of 113: -1, -113

Prime Factorization of 113

The prime factorization of 113 is the product of its prime factors.

Prime Factorization: 1 x 113

In this article, we will learn about the factors of 113 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 113?

The factors of 113 are 1 and 113. As 113 is a prime number that is why it has only two factors 1 and 113.

113 has no other factor as it cannot be divided into equal parts. As far as the factors are concerned they can be only whole numbers.

How To Find the Factors of 113?

You can find the factors of 113 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 113, create a list containing the numbers that are exactly divisible by 113 with zero remainders. One important thing to note is that 1 and 113 are the 113’s factors as every natural number has 1 and the number itself as its factor.

Since 113 is a prime factor it has only 1 and 113 in its factor list.

1 is also called the universal factor of every number. Therefore 1 and 113 are the only factors of 113.

Total Number of Factors of 113

For 113 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 113. 

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:

The factorization of 113 is 1 x 113.

The exponent of 1 and 113 is 1.

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

Therefore, the total number of factors of 113 is 4. 2 are positive and 2 factors are negative.

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 113 by Prime Factorization

The number 113 is a prime number. 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 113 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 113, 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 113 can be expressed as:

\[ 113 = 1 \times 113\]

Factors of 113 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.

113 has only one-factor pair as it has only two factors. The factor pair of 113 is (1, 113).

As this is the only pair that produces 113 as the result of their multiplication.

The negative factor pair of 113 is given as:

\[ -1 \times -113 = 113 \]

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 -113 are called negative factors of 113.

The list of all the factors of 113 including positive as well as negative numbers is given below.

Factor list of 113: 1, -1, 113, and -113

Factors of 113 Solved Examples

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

Example 1

Find the sum of factors of 113.

Solution

Factors of 113 are 1 and 113.

The sum of the factors can be found by adding them both.

Sum = 1 + 113 = 114

Example 2

Find the factors of 113 using prime factorization.

Solution

The prime factorization of 113 is given as:

\[ 113 \div 113 = 1 \]

So the prime factorization of 113 can be written as:

\[ 1 \times 113 = 113 \]

Factors of 112|Factors List| Factors of 114

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