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
 

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:
 

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)
 

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.
 

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.
 

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
 

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)
 

• 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).