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Last updated on January 7th, 2025

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Factors Of 126

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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

Factors Of 126 for US Students
Professor Greenline from BrightChamps

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
 

Professor Greenline from BrightChamps

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:
 

Professor Greenline from BrightChamps

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)
 

Professor Greenline from BrightChamps

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.
 

Professor Greenline from BrightChamps

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.
 

Professor Greenline from BrightChamps

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
 

Professor Greenline from BrightChamps

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)
 

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Common Mistakes and How to Avoid Them in Factors Of 126

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Factors Of 126 Examples

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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?

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Explanation

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Max, the Girl Character from BrightChamps

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?

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Explanation

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Max, the Girl Character from BrightChamps

Problem 3

What is the GCF of 126 and 72?

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Explanation

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FAQs on Factors Of 126

1.Is 126 a factor of 4?

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2.What are the multiples of 126?

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3.Is 126 a perfect cube?

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4.Is 126 a prime number?

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5.What numbers are divisible by 126?

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6.How can children in United States use numbers in everyday life to understand Factors Of 126?

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7.What are some fun ways kids in United States can practice Factors Of 126 with numbers?

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8.What role do numbers and Factors Of 126 play in helping children in United States develop problem-solving skills?

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9.How can families in United States create number-rich environments to improve Factors Of 126 skills?

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Professor Greenline from BrightChamps

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).
     
Professor Greenline from BrightChamps

About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they unlock a world full of possibilities! Our goal is to support kids throughout the United States in mastering key math skills, such as today’s Factors Of 126, with a special emphasis on understanding factors—in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, tracking scores at a Little League baseball game, or budgeting their allowance to buy cool gadgets, understanding numbers builds their confidence for everyday tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in unique ways, we customize our methods to match each child’s style. From the busy streets of New York City to the sunny beaches of California, BrightChamps makes math come alive, bringing it closer to children everywhere. Let’s turn factors into an exciting part of every child’s math adventure!
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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.

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Fun Fact

: She loves to read number jokes and games.

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