Factors of 126 – Easy Division and Prime Factorization | Easy Way

Factors of 126

The factors of 126 are the natural numbers, also called divisors, by which the original number can be evenly divided. 

126 has more than two factors because it is an even composite number. When two natural numbers are multiplied, the result is 126, so such numbers are factors of 126. They may also be common factors to other numbers. Consider the case where 2 is a factor of all even numbers, such as 4, 16, 28, 60, 100, 126, etc. Therefore, a number can be a factor of more than one natural number. However, 1 is the factor of all the numbers.

What are the Factors of -126?

When we multiply two numbers, and we get -126 as a product, those numbers are the factors of -126.

Here is the explanation:

-1 × 126 = -126

 1 × -126 = -126

 -2 × 63 = -126

 2 × -63 = -126

 -3 × 42 = -126

 3 × -42 = -126

 -6 × 21 = -126

 6 × -21 = -126

 -7 × 18 = -126 

 7 × -18 = -126

 -9 × 14 = -126

 9 × -14 = -126

We can get -126 by having (-1, 126), (-2, 63), (-3, 42), (-6, 21), (-7, 18), and (-9,14)as a pair of factors. Similarly, we can also get -126 by having (1, -126), (2, -63), (3, -42), (6, -21), (7, -18), and (9,-14)as a pair of factors.

How to Find the Factors of 126?

Factors divide original numbers uniformly. Hence, we can find the factors of 126 by dividing them by other natural numbers.

126 ÷ 1 = 126

126 ÷ 2 = 63

126 ÷ 3 = 42

126 ÷ 6 = 21

126 ÷ 7 = 18

126 ÷ 9 = 14

126 ÷ 14 = 9

126 ÷ 18 = 7

126 ÷ 21 = 6

126 ÷ 42 = 3

126 ÷ 63 = 2

126 ÷ 126 = 1

Hence, the factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126.

More Factors

Factors Of 120= 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

Factors of 144= 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

Factors of 215=  1, 5, 43 and 215.

Factors of 24= 1, 2, 3, 4, 6, 8, 12, and 24.

Pair Factors of 126

When multiplying two factors in pairs, we call them pair factors.

1 × 126 = 126

2 × 63 = 126

3 × 42 = 126

6 × 21 = 126

7 × 18 = 126

9 × 14 = 126

Hence, the pair factors of 126 are (1, 126), (2, 63), (3, 42), (6, 21), (7, 18), and (9, 14).

Negative pair factors can be written as the product of two negative numbers that equals 126.

-1 × -126 = 126

-2 × -63 = 126

-3 × -42 = 126

-6 × -21 = 126

-7 × -18 = 126

-9 × -14 = 126

As a result, the negative pair factors are as follows: (-1, -126) (-2, -63), (-3, -42) (-6, -21), (-7, -18) and (-9, 14).

Prime Factorization of 126

The prime factors that can divide 126 exactly can be determined since 126 is a composite number. 

The prime factorization of 126 is as follows:

126 ÷ 2 = 63

63 ÷ 3 = 21

21 ÷ 3 = 7

7 ÷ 7 = 1

Hence, the prime factor of 126 is 2, 3, and 7.

Solved Examples

Q.1: What should be multiplied by 21 to produce 126?

Solution: Let x be the number to be multiplied by 21 to get 126.

So, x × 21 = 126

x = 126/21

x = 6

Hence, 6 should be multiplied by 21 to get 126.

Q.2: What is the sum of factors 126?

Solution: Factors of 126 = 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.

Sum of all the factors = 1 + 2 + 3 + 6 + 7 + 9 + 14 + 18 + 21 + 42 + 63 + 126

Sum = 312

Hence, 312 is the required sum.

Q.3: Calculate the greatest common factor of 38 and 126.

Solution: Factors 38 and 126, respectively, are:

Factors of 38 → 1, 2, 19, 38.

Factors of 126 → 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

Hence, the greatest common factor of 38 and 126 are:

GCF (38, 126) = 2

Practice Questions

1. How many divisors of 126 are even?
2. Find the common factors between 126 and 132.
3. The GCF of 98 and 126 is?
4. How many prime factors are there in 126?

FAQ`s