Math Tutor Explains: What are the Factors of 138?

As your math tutor, I’m here to help you understand factors! The factors of 138 are any whole numbers that can be multiplied together to equal exactly 138. In other words, finding the factors of 138 is like breaking it down into all the smaller numbers that, when multiplied, give you 138. Let’s explore this step by step!

Factors of 138: As Taught by a Math Tutor

Methods

What are the Factors of 138?

As your math tutor, I’m here to guide you through the different types of factors of 138. Understanding factors is key to mastering multiplication, division, and prime numbers. Here’s a breakdown:

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

• Sum of Factors of 138: 288

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

• Prime Factors of 138: 2, 3, 23

• Prime Factorization of 138: 2^1 × 3^1 × 23^1

There are two main ways a math tutor would explain how to find the factors of 138: using factor pairs and prime factorization. Let’s explore both!

The Factor Pairs of 138

As your math tutor, I’m here to help you break down factor pairs of 138 step by step!

Factor pairs of 138 are any two numbers that, when multiplied together, equal 138. The question to ask is “what two numbers multiplied together equal 138?” Every factor can be paired with another factor, and multiplying the two will result in 138.

To find the factor pairs of 138, follow these steps:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 138. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 138 by the smallest prime factor, in this case, 2:

138 ÷ 2 = 69

2 and 69 will make a new factor pair.

Step 3:

Repeat Steps 1 and 2, using 69 as the new focus. Find the smallest prime factor that isn’t 1, and divide 69 by that number. In this case, 3 is the new smallest prime factor:

69 ÷ 3 = 23

Remember that this new factor pair is only for the factors of 69, not 138. So, to finish the factor pair for 138, you’d multiply 2 and 3 before pairing with 23:

2 x 3 = 6

Step 4:

Repeat this process until there are no longer any prime factors larger than one to divide by. At the end, you should have the full list of factor pairs.

Here are all the factor pairs for 138:

(1, 138), (2, 69), (3, 46), (6, 23)

So, to list all the factors of 138: 1, 2, 3, 6, 23, 46, 69, 138

The negative factors of 138 would be: -1, -2, -3, -6, -23, -46, -69, -138

Now you’ve got it! A math tutor would always encourage you to practice with different numbers to reinforce your understanding of factor pairs. Try another one!

Prime Factorization of 138

To find the prime factorization of 138, we break it down step by step until only prime factors remain. Then, we express 138 as a product of these prime factors multiplied together. Let’s go through the process and simplify it like a math tutor would!

The process of finding the prime factorization of 138 only has a few differences from the above method of finding the factors of 138. Instead of ensuring we find the right factor pairs, we continue to factor each step until we are left with only the list of smallest prime factors greater than 1.

Here are the steps for finding the prime factorization of 138:

Step 1:

Find the smallest prime number that is larger than 1, and is a factor of 138. For reference, the first prime numbers to check are 2, 3, 5, 7, 11, and 13. In this case, the smallest factor that’s a prime number larger than 1 is 2.

Step 2:

Divide 138 by the smallest prime factor, in this case, 2

138 ÷ 2 = 69

2 becomes the first number in our prime factorization.

Step 3:

Repeat Steps 1 and 2, using 69 as the new focus. Find the smallest prime factor that isn’t 1, and divide 69 by that number. The smallest prime factor you pick for 69 will then be the next prime factor. If you keep repeating this process, there will be a point where there will be no more prime factors left, which leaves you with the prime factors for prime factorization.

So, the unique prime factors of 138 are: 2, 3, 23

Math Tutor Suggests: Find the Factors of Other Numbers

Practice your factoring skills by exploring how to factor other numbers, like the ones below:

Factors of 3 - The factors of 3 are 1, 3

Factors of 62 - The factors of 62 are 1, 2, 31, 62

Factors of 73 - The factors of 73 are 1, 73

Factors of 39 - The factors of 39 are 1, 3, 13, 39

Download FREE Math Resources

Take advantage of our free downloadable resources and study materials for at-home learning.

8 Math Hacks and Tricks to Turn Your ‘Okay’ Math Student Into a Math Champion!

One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.

Get PDF

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

Get PDF

Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?

A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.

Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.

Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!

Start 7-Day Free Trial