What Are the Factors of 10? A Simple Math Guide

Have you ever wondered how to divide 10 evenly? In this guide, we’ll explore the factors of 10 in a simple and fun way. Whether you’re a parent helping your child or a student learning on your own, understanding factors is an important math concept that will make many other math problems easier to solve. Let’s get started!

Understanding the factors of 10 is essential for building a strong foundation in number theory, algebra, and real-world problem-solving.

Factors of 10 are the list of integers that we can split evenly into 10. There are overall 4 factors of 10 ,like 1, 2, 5 and 10 where 10 is the biggest factor. The Prime Factors of 10 are 1, 2, 5, 10 and its Factors in Pairs are (1, 10) and (2, 5).

What Are Factors?

In math, a factor is any number that divides another number exactly, without leaving a remainder. Factors are the building blocks of numbers. To understand this better, let’s look at the example of 6:

• The factors of 6 are 1, 2, 3, and 6.
• That’s because:
  • 1 × 6 = 6
  • 2 × 3 = 6

Simply put, factors are numbers that fit perfectly into another number. They help us break down numbers into smaller, more manageable parts, which is useful for multiplication, division, and even fractions!

How to Find the Factors of 10

Now let’s learn how to find the factors of 10. Finding factors is easy if you follow these simple steps:

1. Start with 1: Every number is divisible by 1, so 1 is always a factor.
2. Check 2: Does 2 divide 10 evenly? Yes, because 10 ÷ 2 = 5.
3. Check 3: Does 3 divide 10 evenly? No, because 10 ÷ 3 = 3 with a remainder of 1. So, 3 is not a factor of 10.
4. Check 4: Does 4 divide 10 evenly? No, 10 ÷ 4 = 2 with a remainder. So, 4 is not a factor of 10.
5. Check 5: Does 5 divide 10 evenly? Yes, because 10 ÷ 5 = 2.
6. Finally, check 10: Every number divides evenly by itself, so 10 ÷ 10 = 1.

So, the factors of 10 are: 1, 2, 5, and 10.

The Factors of 10

The prime factorization of 10 breaks it into its prime components: 2 and 5, which are irreducible primes.

Here’s a quick list of the factors of 10:

List of Positive and Negative Factors

What Are Factor Pairs?

A factor pair is simply a combination of two factors that multiply together to give the number. The factor pairs of 10 are:

• (1, 10) because 1 × 10 = 10
• (2, 5) because 2 × 5 = 10

These factor pairs help us understand how two numbers can work together to create the number 10. Factor pairs are useful for division, as they show us all the possible ways we can divide 10 evenly.

Prime Factorisation of 10

The prime factorisation of a number breaks it down into prime numbers—numbers greater than 1 that can only be divided by 1 and themselves. To find the prime factorisation of 10, let’s break it down step by step:

• 10 can be divided by 2, which gives 5.
• Both 2 and 5 are prime numbers.

So, the prime factorisation of 10 is:

[10 = 2 times 5]

Prime factorisation is a useful way to understand the building blocks of a number, especially when you need to solve problems involving multiplication or division.

Factor Tree of 10

A factor tree of 10 is a visual representation that decomposes 10 into its prime factors. This aids in more clearly understanding how to decompose a number into prime factors. Below are the steps to create a factor tree for 10:

Step One. Start with numbers:

Start from the number 10 at the top of the tree.

Step Two. Divide by the smallest prime number

• The smallest prime number is 2.
• Divide 10 by 2: 10 ÷ 2 = 5
• Write 2 as a branch connected to 10, and write 5 as the next level.

Step 3. Identify the next prime number:

• The number 5 is a prime number and cannot be further decomposed, so we stop the decomposition process.

Step Four. Complete the factor tree:

Here, 10 splits into 2 and 5, which are both prime factors. Factor trees are helpful because they give a clear visual representation of how a number can be broken down into smaller parts.

This method provides a simple and systematic way to decompose numbers, helping you better understand the prime factorization of 10.

Solved Examples on Factors of 10

Let’s look at some examples to make sure we understand the concept of factors.

Example 1: Find the factors of 10

We already know that the factors of 10 are 1, 2, 5, and 10. These are the numbers that divide 10 exactly.

Example 2: Factor Pairs of 10

The factor pairs of 10 are:

• (1, 10): 1 × 10 = 10
• (2, 5): 2 × 5 = 10

Example 3: Prime Factorisation of 10

The prime factorisation of 10 is:
[10 = 2 times 5]
This tells us that the number 10 is made up of the prime numbers 2 and 5.

Example 4: Use Factors in Real Life

Imagine you have 10 apples and want to share them equally among your friends. You could divide them in the following ways:

• 1 apple per friend: You need 10 friends.
• 2 apples per friend: You need 5 friends.
• 5 apples per friend: You need 2 friends.
• 10 apples per friend: You need 1 friend.

These are examples of how factors work in real life. They show us how to divide objects or quantities evenly, which is useful when sharing or organizing things.

Mastering Factors and Multiples

Understanding how to identify factors is a core competency within the Common Core State Standards for Mathematics. This skill is primarily introduced in Grade 4 (4.OA.B.4), where students learn to find all factor pairs for whole numbers in the range 1–100. It is further refined in Grade 6 (6.NS.B.4) as students apply these concepts to find the Greatest Common Factor (GCF) and solve real-world problems.

Factor Reference Table

FAQ: Factors of 10

Q1: How to find factors of a number?

Thus, to find all the factors of a number, find all the pairs of numbers that, when multiplied, give the given number as a product. As a result, the factors of 8 are 1, 2, 4, 8. The factors of 18 are 1, 2, 3, 6, 9, and 18. We can find the factors of a number by dividing the number by all possible divisors.

Q2: What is the sum of all factors of 10?

1+2+5+10=181+2+5+10=18.

Q3: How many factors do 10 and 100 have?

The number 10 has 4 factors, such as 1, 2, 5 and 10.
The number 100 has 9 factors, such as 1, 2, 4, 5, 10, 20, 25, 50, and 100.

Q4: Can factors be decimals?

No, factors are always whole numbers.

Q5: What is the difference between prime and composite numbers?

Prime numbers have two factors; composite numbers have more than two.

Q6:What is the least common factor (LCF) of 6 and 10?

The term “least common factor” is unconventional. All integers share 1 as their smallest common factor.

If you meant least common multiple (LCM) of 6 and 10, it is 30 (smallest number divisible by both).

Q7: What is the greatest common factor (GCF) of 10 and 8?

The GCF of 10 and 8 is 2.

Explanation: Factors of 10: 1, 2, 5, 10; factors of 8: 1, 2, 4, 8. The largest common factor is 2.

Q8: What is the least common factor (LCF) of 10 and 15?

The smallest common factor is 1.

If you meant LCM, it is 30 (smallest number divisible by both).

Q9:What is the greatest common factor (GCF) of 6 and 10?

The GCF of 6 and 10 is 2.

Explanation: Factors of 6: 1, 2, 3, 6; factors of 10: 1, 2, 5, 10. The largest common factor is 2.

Q10:What is the greatest common factor (GCF) of 8 and 10?

This is the same as question 2. The GCF of 8 and 10 is 2.

Q11: What is the greatest common factor (GCF) of 10 and 15?

The GCF of 10 and 15 is 5.

Explanation: Factors of 10: 1, 2, 5, 10; factors of 15: 1, 3, 5, 15. The largest common factor is 5.

Q12:What is the lowest common factor of 6 and 10?

The smallest common factor is 1.

If you meant LCM, it is 30.

Conclusion

Now you know that the factors of 10 are 1, 2, 5, and 10. You’ve learned how to find factors, understand prime factorisation, and use factor pairs. We also saw how a factor tree can help us break down numbers into their prime factors.

By understanding factors, you can tackle a wide range of math problems, including division, multiplication, and even fractions! Keep practicing, and soon you’ll be able to find the factors of any number quickly and easily.

Want to learn more about factors? Try finding the factors of other numbers from Wukong math and improve your math skills! The more you practice, the better you’ll get at understanding how numbers work together.

Demi | WuKong Math Teacher

I am an educator from Yale University with ten years of experience in this field. I believe that with my professional knowledge and teaching skills, I will be able to contribute to the development of Wukong Education. I will share the psychology of children’s education and learning strategies in this community, hoping to provide quality learning resources for more children.