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Factors of 133: Prime Factorization, Methods, and Examples

The factors of 133 are the group of natural numbers that can be completely divided by 133. The factors of 133 can also be defined as the numbers in pairs that when multiplied together result in 133 as their product. 133 is a composite number with 4 factors. The highest or biggest factor of 133 is 133.

Factors of 133

Here are the factors of number 133.

Factors of 133: 1, 7, 19, 133

Negative Factors of 133

The negative factors of 133 are similar to its positive factors, just with a negative sign.

Negative Factors of 133: -1, -7, -19, and -133

Prime Factorization of 133

The prime factorization of 133 is the way of expressing its prime factors in the product form.

Prime Factorization: 7 x 19

In this article, we will learn about the factors of 133 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 133?

The factors of 133 are 1, 7, 19, and 133. All of these numbers are the factors as they do not leave any remainder when divided by 133.

The factors of 133 are classified as prime numbers as all of them are its prime factors. The prime factors of the number 133 can be determined using the technique of prime factorization.

How To Find the Factors of 133?

You can find the factors of 133 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 133, create a list containing the numbers that are exactly divisible by 133 with zero remainders. One important thing to note is that 1 and 133 are 133’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 133 are determined as follows:

\[\dfrac{133}{1} = 133\]

\[\dfrac{133}{7} = 19\]

\[\dfrac{133}{19} = 7\]

\[\dfrac{133}{133} = 1\]

Therefore, 1, 7, 19, and 133 are the factors of 133.

Total Number of Factors of 133

For 133 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 133. 

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 133 is given as:

Factorization of 133 is 1 x 7 x 19.

The exponent of 1, 7, and 19 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 133 is 8. 4 are positive and 4 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 133 by Prime Factorization

The number 133 is a 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 133 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 133, 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 133 can be expressed as:

133 = 7 x 19

Factors of 133 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 133, the factor pairs can be found as:

 1 x 133 = 133 

7 x 19 = 133

The possible factor pairs of 133 are given as (1, 133) and (7, 19 ).

All these numbers in pairs, when multiplied, give 133 as the product.

The negative factor pairs of 133 are given as:

-1 x -133 = 133

-7 x -19 = 133 

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, -7, -19, and -133 are called negative factors of 133.

The list of all the factors of 133 including positive as well as negative numbers is given below.

Factor list of 133: 1, -1, 7, -7, 19, -19, 133, and -133

Factors of 133 Solved Examples

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

Example 1

How many factors of 133 are there?

Solution

The total number of Factors of 133 is 4.

Factors of 133 are 1, 7, 19, and 133.

Example 2

Find the factors of 133 using prime factorization.

Solution

The prime factorization of 133 is given as:

133 $\div$ 7 = 19 

19 $\div$ 19 = 1 

So the prime factorization of 133 can be written as:

7 x 19 = 133 

Factors of 132|Factors List| Factors of 134

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