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Factors of 138: Prime Factorization, Methods, and E138amples

The number 138 is an even number therefore it has more than two factors. Hence 138 is a composite number. The factors of 138 form a list of integers that are completely divisible by 138. 138 has 8 factors in total.

Factors of 138

Here are the factors of number 138.

Factors of 138: 1, 2, 3, 6, 23, 46, 69, 138

Negative Factors of 138

The negative factors of 138 are similar to its positive factors, just with a negative sign.

Negative Factors of 138: -1, -2,- 3, -6, -23, -46, -69, -138

Prime Factorization of 138

The prime factorization of 138 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 3 x 23

In this article, we will learn about the factors of 138 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 138?

The factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138. All of these numbers are the factors as they do not leave any remainder when divided by 138.

The factors of 138 are classified as prime numbers and composite numbers. The prime factors of the number 138 can be determined using the prime factorization technique.

How To Find the Factors of 138?

You can find the factors of 138 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 138, create a list containing the numbers that are e138actly divisible by 138 with zero remainders. One important thing to note is that 1 and 138 are the 138’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 138 are determined as follows:

\[\dfrac{138}{1} = 138\]

\[\dfrac{138}{2} = 69\]

\[\dfrac{138}{3} = 46\]

\[\dfrac{138}{6} = 23\]

\[\dfrac{138}{138} = 1\]

The quotient, as well as the divisor, are considered as the factors of number 138. Therefore, 1, 2, 3, 6, 23, 46, 69, and 138 are the factors of 138.

Total Number of Factors of 138

For 138 there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 138. 

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 e138ponent form.
  3. Add 1 to each of the e138ponents of the prime factor.
  4. Now, multiply the resulting e138ponents 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 138 is given as:

The factorization of 138 is 1 x 2 x 3 x 23.

The exponents of all the factors are 1.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors of 138 is 16. 8 are positive and 8 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, the smallest prime factor.

Factors of 138 by Prime Factorization

The number 138 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 138 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 138, 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 138 can be expressed as:

\[  138 = 2 \times 3 \times 23\]

Factors of 138 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 of the given numbers.

For 138, the factor pairs can be found as:

\[ 1 \times 138 = 138 \]

\[ 2 \times 69 = 138 \]

\[ 3 \times 46 = 138 \]

\[ 6 \times 23 = 138 \]

The possible factor pairs of 138 are given as (1, 138), (2, 69), (3, 46), and (6, 23).

All these numbers in pairs, when multiplied, give 138 as the product.

The negative factor pairs of 138 are given as:

\[ -1 \times -138 = 138 \]

\[ -2 \times -69 = 138 \]

\[ -3 \times -46 = 138 \]

\[ -6 \times -23 = 138 \]

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, -3, -6, -23, -46, -69, and -138 are called negative factors of 138.

The list of all the factors of 138 including positive as well as negative numbers is given below.

Factor list of 95: 1, -1, 2, -2, 3, -3, 6, -6, 23, -23, 46, -46, 69, -69, 138, and -138

Factors of 138 Solved Examples

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

Example 1

How many factors of 138 are there?

Solution

The total number of Factors of 138 is 8.

Factors of 138 are 1, 2, 3, 6, 23, 46, 69, and 138.

Example 2

Find the factors of 138 using prime factorization.

Solution

The prime factorization of 138 is given as:

\[ 138 \div 2 = 69 \]

\[ 69 \div 3 = 23 \]

\[ 23 \div 23 = 1 \]

So the prime factorization of 138 can be written as:

\[ 2 \times 3 \times 23 = 138 \]

Factors of 137|Factors List| Factors of 139

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