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Factors of 131: Prime Factorization, Methods, and Examples

The number 131 is a prime number that can only be divided by 1 and 131 itself. 131 is the biggest factor of number 131. In general, factors are the numbers that divide the given number evenly without any remainder. In the case of 131, only two numbers satisfy this condition which are 1 and 131.

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 131

Here are the factors of number 131.

Factors of 131: 1 and 131

Negative Factors of 131

The negative factors of 131 are similar to its positive factors, just with a negative sign.

Negative Factors of 131: -1 and -131

Prime Factorization of 131

The prime factorization of 131 is the way of expressing its prime factors in the product form.

Prime Factorization:1 x 131

In this article, we will learn about the factors of 131 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 131?

The factors of 131 are 1 and 131. All of these numbers are the factors as they do not leave any remainder when divided by 131.

The factors of 131 are classified as prime numbers and composite numbers. The prime factors of the number 131 can be determined using the prime factorization technique.

How To Find the Factors of 131?

You can find the factors of 131 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 131, create a list containing the numbers that are exactly divisible by 131 with zero remainders. One important thing to note is that 1 and 131 are the 131’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 131 are determined as follows:

\[\dfrac{131}{1} = 131\]

\[\dfrac{131}{131} = 1\]

Therefore,1 and 131 are the factors of 131.

Total Number of Factors of 131

For 131 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 131. 

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 131 is given as:

Factorization of 131 is 1 x 131.

The exponent of 1 and 131 is 1.

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

Therefore, the total number of factors of 131 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 131 by Prime Factorization

The number 131 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 131 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 131, 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 131 can be expressed as:

\[  131 = 1 \times 131\]

Factors of 131 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 131, the factor pair can be found as:

\[ 1 \times 131 = 131 \]

It has only a one-factor pair as 131 is a prime number.

The possible factor pair of 131 is (1, 131).

The negative factor pair of 131 is given as:

\[ -1 \times -131 = 131 \]

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 -131 are called negative factors of 131.

The list of all the factors of 131 including positive as well as negative numbers is given below.

Factor list of 131: 1, -1, 131, and -131

Factors of 131 Solved Examples

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

Example 1

How many factors of 131 are there?

Solution

The total number of Factors of 131 is m.

Factors of 131 are 1 and 131.

Example 2

Find the sum of factors of 131.

Solution

The sum of factors of 131 is 1 + 131 = 132.

Therefore sum is equivalent to 132.

Factors of 130|Factors List| Factors of 132

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