Factors of 126
2026-02-28 11:17 Diff
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Last updated on December 11, 2025

A number that divides another number exactly without leaving any remainder is called a factor of the given number. Factors play an important role in various real-life situations, such as deciding the best time to schedule work shifts and events

What are the Factors of 126?

Factors often come in pairs. There are several methods to determine them, which we will explore later. For now, let's focus on the factors of 126, which are listed below:


Negative factors of 126: -1, -2, -3, -6, -7, -9, -14, -18, -21, -42, -63, -126
Prime factors of 126: 2, 3, and 7
Prime factorization of 126: 2 × 3² × 7
The sum of factors of 126: 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126 = 312
 

How to Find the Factors of 126?

For finding factors, students use different methods for easy calculation. A few commonly used methods are as follows:

  • Multiplication Method
  • Division Method
  • Prime Factorization Method.

So, here we discuss a detailed explanation of the following methods:
 

Finding Factors Using Multiplication Method

In the multiplication method, we will find the numbers that multiply together to give the value of 126. We will check the factors step by step:


Step 1: Start by multiplying numbers that give 126. Begin with 1 and continue with other numbers:


1 × 126 = 126
2 × 63 = 126
3 × 42 = 126
6 × 21 = 126
7 × 18 = 126
9 × 14 = 126


Step 2: The factor pairs of 126, derived from the multiplication results, are as follows.


Step 3: The positive factor pairs of 126 are: (1, 126) (2, 63) (3, 42) (6, 21) (7, 18) (9, 14)


Step 4: The negative factor pairs of 126 are: (-1, -126) (-2, -63) (-3, -42) (-6, -21) (-7, -18) (-9, -14)
 

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Finding Factors Using Division Method

To find the factors of 126, we will divide the number by smaller integers and check if there is no remainder.


Step 1: Start by dividing 126 by 1. Since 126 ÷ 1 = 126, 1 is a factor of 126.


Step 2: Continue dividing 126 by the next integers, checking if the result is a whole number (i.e., no remainder). For 126, the divisors (factors) are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126, as 126 can be divided evenly by these numbers.
 

Prime Factors and Prime Factorization

The prime factors of 126 are 2, 3, and 7. The prime factors can be found using the methods given below:

  • Prime Factorization
  • Factor Tree

Prime factorization is a method in which we break down a number into its prime factors. 


Since 2 is the smallest prime number, we start dividing by it and continue dividing by other prime numbers.


126 ÷ 2 = 63
63÷3 = 21
21÷3 = 7
7 ÷ 7= 1


 The prime factorization of 126 is :


 126 = 21 × 32 × 71


Thus, 126 can be broken down into the prime factors 2, 3, and 7.
 

Factor Tree

A factor tree is a graphical representation of breaking a composite number into its prime factors. It is an easy method to find the prime factors of any number.


Step 1: 126 divided by 2 gives us the quotient 63.


Step 2: Since 63 is not a prime number, it can be further divided. Dividing 63 by 3 gives 21, which can then be divided by 3 again to give 7.


The prime factorization of 126 is:


126 = 21 × 32 × 71
 

Factor Pairs

Every number has either a positive or negative factor. Let us look at those sets of factors.


Positive pair Factors:(1,126), (2,63), (3,42), (6,21), (7,18), and (9,14)
Negative pair Factors:  (-1,-126), (-2,-63), (-3,-42), (-6,-21), (-7,-18), and (-9,-14)
 

Common Mistakes and How to Avoid Them in Factors Of 126

Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
 

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Problem 1

Lisa wants to find the sum of odd factors of 126. How can we help her with the calculation?

Okay, lets begin

The sum of odd factors of 126 is 104
 

Explanation

The sum of odd factors is 104. An easy way to find the answer is to list all factors of 126 and identify the odd factors. Then, add these factors together. 


The factors of 126 are: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
The odd factors of 126 are: 1, 3, 7, 9, 21, and 63.
The sum of odd factors: 1 + 3 + 7 + 9 + 21 + 63 = 104.

Well explained 👍

Problem 2

The teacher has assigned Kevin the task of finding the smallest prime factor of 126. How can we help him with the calculation?

Okay, lets begin

 2 is the smallest prime factor of 126
 

Explanation

 A prime number has only two factors, 1 and the number itself. To find the smallest prime factor of 126, just list all the prime factors of 126.


Prime factors of 126: 2, 3, and 7. In this list, 2 is the smallest prime number. Hence, the answer is 2.
 

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Problem 3

What is the GCF of 126 and 72?

Okay, lets begin

The GCF of 126 and 72 is 18. 
 

Explanation

The greatest common factor is the largest number which divides both numbers evenly. The GCF of 126 and 72 is 18. The following steps make it easy to understand: 


Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Common factors of 126 and 72: 1, 2, 3, 6, 9, 18.


GCF of 126 and 72: 18.
 

Well explained 👍

FAQs on Factors Of 126

1.Is 126 a factor of 4?

No, 126 is not a factor of 4. Factors are numbers that divide the given number completely. When 126 is divided by 4, it leaves a remainder.

2.What are the multiples of 126?

Multiples of 126 are the numbers that we get when 126 is multiplied by other numbers. For example, the multiples of 126 are 126 (1 × 126), 252 (2 × 126), 378 (3 × 126), 504 (4 × 126), and so on.
 

3.Is 126 a perfect cube?

No, 126 is not a perfect cube. A perfect cube is a number that is the result of multiplying the same number three times.
 

4.Is 126 a prime number?

No, 126 is not a prime number. Prime numbers are numbers with only two factors, 1 and the number itself. 126 is a composite number. Composite numbers have more than two factors.

5.What numbers are divisible by 126?

The numbers that give zero as the remainder are the numbers that are divisible by 126. These are the multiples of 126. For example, the multiples of 126 are 126 (1× 126), 252 (2 × 126), 378 (3 × 126), 504 (4 × 126), and so on.
 

Important Glossaries For Factors Of 126

  • Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.
  • Prime Factors: Prime factors of a number are a set of prime numbers that multiply together to give the original number. For 126, the prime factors are 2, 3, and 7.
  • Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.