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What Is A Factor In Math? - Mastering the Basics of Factors

Learn about factors in math and how to find them with examples. Understand the importance of factors in mathematical operations and problem-solving.
13 minutes
What Is A Factor In Math? - Mastering the Basics of Factors
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Factors are essential to understanding division and other operations with integers.

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What Is A Factor in Math?

A factor is a number that can divide a given number perfectly without any remainder.

For example, the factors of 10 are 1, 2, 5, and 10 because each of these numbers can divide 10 perfectly. Note that the factor of a number must be an integer, which can be positive or negative. (i.e., a whole number, not a fraction or decimal).

For example, the number 1.5 is not a factor of 10 because it is not an integer. The number 2, on the other hand, is a factor of 10 because it is an integer and divides 10 without leaving a remainder.

A factor can also be multiplied by another number to create a given number. In other words, it's one of the numbers that make up a multiplication table.

For example, 3 and 5 are factors of 15 because 3 x 5 = 15

So, if we're looking at the multiplication problem 7 x 2 = 14, the factors would be 7 and 2.

In that sense, when you're trying to find the factors of a number, just look for all the numbers that can be multiplied together to create that number! And there you have all the factors of the number.

Why Finding Factors of A Number in Math Is Important

In math, factors are important and come into play when dealing with division. In fact, the whole division operation is based on finding the factors of a number!

To divide one number by another, you need to find how many times the divisor can divide the number evenly without leaving a remainder.

For example, if we want to divide 10 by 2, we need to find how many times 2 can divide 10.

We can do this by finding the factors of 10 and then seeing how many of those factors are also factors of 2.

How To Find Factors In Math

To find the factors of a number, you can use the division method or factor tree method. With a little practice, you can use these methods to find the factors of any number.

To use the division method, simply divide the number by every natural number between 1 and that particular number until you find a number that divides evenly into the original number, which can be both positive and negative numbers. 

In the case of numbers above 10, you are likely to find more than two factors explaining these numbers. Isn’t it also interesting to know that every number, apart from 1 and 0, has at least two factors and that there can be both negative and positive factors?

Example: Let's find the factors of 24 using the division method:

24 ÷ 1 = 24 (1 is a factor of 24)

24 ÷ 2 = 12 (2 is a factor of 24)

24 ÷ 3 = 8 (3 is a factor of 24)

24 ÷ 4 = 6 (4 is a factor of 24)

24 ÷ 6 = 4 (6 is a factor of 24)

24 ÷ 8 = 3 (8 is a factor of 24)

24 ÷ 12 = 2 (12 is a factor of 24)

24 ÷ 24 = 1 (24 is a factor of 24)

From the foregoing, we can see that the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Also, notice the factor pairs that make up the factors of 24: 12 and 1, 12 and 2, 8 and 3, and so on.

To wrap it up, don't forget about how prime numbers are connected to factors. A prime number is a number that can only be divided by 1 and itself (the same number). For example, the numbers 2, 3, 5, 7, 11, 13, 17, and 19 are prime numbers.

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When to Consider Getting a Tutor

As always, mastering factors in math will take time and practice. Like anything else, the more you work on it, the better you will become.

But if you find yourself or your child struggling with finding factors, algebraic expressions, or any other math concepts, then getting a tutor might be a good idea.

What to Expect When Working with an Online Tutor at Learner

Online classes with a tutor can be just as effective as in-person classes, and in many ways, they can be even more so!

When working one-on-one with a tutor, especially an online math tutor at Learner, there are a few things you can expect:

A focus on your individual needs

In a one-on-one setting, the tutor can focus on your unique needs and tailor the lesson to your learning style.

Greater accountability

When it's just you and the tutor, you're more likely to stay engaged and focused on the lesson.

Greater flexibility

Online classes can be scheduled at a time that's convenient for you, even if it's outside of traditional school hours.

Fun and interactive lessons

At Learner, we believe that learning should be fun! Our online math tutors teach their lessons in a variety of ways that are interactive and interesting.

Who Is A Factor Tutor?

A factor tutor is an expert in math who helps students understand the idea of factors. Factors are an important part of math, but there isn't a specific kind of math tutor who only works with them. Factors are usually taught in elementary school. Depending on the school and district, it can be introduced as early as the 4th grade.

A factor tutor helps students get a good grasp of operations that use factors like multiplication, division, and prime factorization. A factor tutor can also help students learn quick and easy ways to find factors.

If you or your child is struggling with factors, or if you simply want to give them a head start in math, consider working with an elementary school or 4th-grade math tutor to start, and depending on their starting point, a high school tutor can still get them caught up.

Get a Confidence Boost With Schoolwork, Contact a Learner Tutor. Take the Quiz to Find The Right Tutor

How To Find Factors In Math

Factors are a fundamental concept in mathematics, and for this reason, every student must have a strong understanding of factors and how to find them. Methods for finding factors include the division method and the multiplication method.

In the division method, you simply divide the number by every number between 1 and itself until you find a number that divides evenly into the original number.

For example, let's find the factors of 12 using the division method:

12 ÷ 1 = 12

12 ÷ 2 = 6

12 ÷ 3 = 4

12 ÷ 4 = 3

12 ÷ 6 = 2

12 ÷ 12 = 1

You can deduce that the factors of 12 are 1, 2, 3, 4, 6, and 12. These are all natural numbers that perfectly divide into 12 with no remainder.

Need more help? Consider signing up for an online math class at Learner! Our expert tutors can help you master factors, understand algebraic expressions, and any other math concept you're struggling with.

Soft Skills You Should Look Out For In An Online Tutor.

Soft skills are an integral part of any work culture and should never be overlooked. When present, soft skills make a tutor effective in an online setting.

Here are a few of the most essential qualities to look for:


Math concepts can be tricky, and it can take some time to master them. Look out for a tutor who will have the patience to work with you until you understand the concept.

A parent, Sharad has experienced the patience of Learner tutors firsthand and has this to say:

"John is an exceptional teacher who will have the patience to make sure that his student understands the concepts before he gets to solving the problem. My son enjoys his class and is becoming increasingly fond of math. Highly recommend John!"


Since there is no one-size-fits-all approach to tutoring, it's crucial to find a creative tutor who can tailor their lessons to your unique needs.


With online tutoring, you have the flexibility to schedule lessons at a time that's convenient for you.

Hear what Ryan said about his experience at Learner

"It's great for me, it has a flexible schedule. And the tutors are amazing. My current tutor, Gerald has been an amazing help for my algebra 2 class."

Clear communication

It’s crucial for online tutors to communicate clearly so that students can understand their lessons.


You want to work with a tutor who is excited to help you learn and considers it a personal challenge to help you succeed.

See what Maria says about her Learner math tutor:

"I needed a tutor for math and was paired with John Mooney. He goes above and beyond to make sure you understand your work. He is amazing. Anytime I have a question, he answers quickly. He has a great YouTube channel that's also helpful. I highly recommend him. I went from being afraid to take a math class to loving math because of John."

Keep these qualities in mind if you're looking for an online math tutor. We only work with the best tutors at Learner, so you can be confident that you're getting high-quality help.

Ready to get started? Take the quiz to connect with us and schedule a lesson with one of our tutors today!

Skills and Experience to Look for in a Factors Tutor

On a practical level, certain skills and qualities make online tutors more effective. Consider looking out for these hard skills when interviewing tutors for the role.

A strong understanding of factors

To teach others about factors, the teacher must have a strong understanding of the concept themselves.

A solid math foundation

Look for a teacher with a strong math foundation. The immense knowledge they have will enable them to break down concepts and explain them in a way that's easy for students to understand.

Joey has only praise for his well-versed Learner tutor:

“Very helpful with the school that I've been struggling with. I would recommend to others that could use the help. My performance in math has substantially increased with the help of my amazing tutor. He knows exactly what he's talking about and will make sure the message gets across so that you're actually learning. I'm very thankful we found this platform and will continue to use it as I need it.”

Has experience teaching factors

While the teacher needs to have a strong understanding of the concept, it's also necessary for them to have experience teaching it. This will ensure they know how to communicate the material to students effectively.

The ability to adapt to different learning styles

Each student learns differently. The teacher must be able to adapt their teaching style to fit each student's individual needs.

Catty says this about her Learner tutor:

"A very pleasing, and tailored experience. My tutor Andrew, is very knowledgeable, and helped me dive deeper into the subject." 

A deep understanding of the curriculum

To be an effective teacher, it's crucial to have a deep understanding of the curriculum. With such in-depth knowledge, the teacher will be able to prepare students well for tests and ensure they learn everything.

"My son was struggling in algebra 1, after 1 session with his tutor, Bright, he started getting As and Bs in his tests and quizzes. He went from a D+ to an A- on his report card." 

Red Flags to look out for when considering a factors teacher

Math tutoring is a big commitment, both in terms of time and money. You want to be sure that you're working with a qualified tutor who will be effective in helping you learn. Here are a few red flags to look out for when considering a factor tutor:

Lack of experience

You want to be sure that the teacher you're working with has experience teaching math, and specifically, factors. Otherwise, they may not be able to communicate the material to you effectively.

Inability to adapt to different learning styles

If the tutor is unable to adapt their teaching style to fit your individual needs, it's likely that you won't get the most out of your lessons.

Lack of understanding of the curriculum

If the tutor doesn't have a deep understanding of the curriculum, they won't be able to effectively prepare you for exams and ensure that you're learning all the material.

Unwillingness to answer questions

If the tutor is resistant to answering your questions, it's likely that you're not getting the help you need.

Rigidity in teaching style

When a tutor is unwilling to try new methods or approaches, it's likely that you won't be able to learn effectively.

When looking for a tutor, be sure to avoid these red flags. By working with a qualified and experienced tutor, you'll be able to get the most out of your lessons and effectively learn the material.

Questions to ask a potential Factor Tutor

It's important to ask the right questions when you interview potential tutors so that you have the best chance of finding a good fit. Here are some questions to ask a potential factor tutor:

  • How much experience do you have teaching math?
  • Do you have experience teaching factors specifically?
  • How well do you understand the curriculum?
  • How can you adapt your teaching style to fit each student's needs?
  • Are you willing to answer any questions I have?
  • What methods or approaches do you use when teaching?
  • Are you open to trying new methods or approaches if I do not understand something?

Qualified and experienced teachers will always be open to answering your questions. Their answers to your questions will give you a good sense of how well they understand the material and how effective they'll be in helping you learn.

What to Expect When Working with an Online Tutor At Learner

From the moment you contact us, we will work with you to find the perfect tutor for your unique needs. We'll consider your location, schedule, and learning goals to find a tutor who is the best fit for you.

Our online tutors are all experienced professionals who are passionate about teaching. The best part is that Learner tutors are patient, supportive, and committed to helping you reach your goals.

Be assured that our tutors will never give up on you and will always be available to answer your questions.

Get ready to ace your exams with the help of our online tutors!

Ready to schedule that free session?

Take the next step with our matching quiz.

Frequently Asked Questions

What is a factor?

A factor is a number that can be divided evenly into other numbers. This concept is taught in elementary school to build upon other more complex math concepts. 

Who is an online factors tutor?

A professional math tutor who teaches factors online is called an online factors tutor. But for a more specific search, look for an elementary school math tutor or a 4th-grade math tutor to start, and if need be, a high school math tutor to get your student caught up. 

How can an online tutor help me learn factors?

An online tutor can help you learn factors by giving you personalized lesson plans and one-on-one help.

Get started with a custom-matched tutor for your child.

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About the author:

Mike developed his passion for education as a math instructor at Penn State University. He expanded his educational experience launching and running an Executive Education business - training over 100,000 students per year. As the CEO of Learner, Mike focuses on accelerating learning and unleashing the potential of students. 

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