Factors of 126—with division and prime factorization

Factors of 126

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.

Factors of 126

What are Factors of -126?

When we multiply two numbers, and we get -126 as a product, that 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 it 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 216= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.

Pair Factors of 126

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

Factors of 126 by prime factorization

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.

Prime factorization of 126 = 2 × 3 × 3 × 7Exponential form = 21 × 32 × 71

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 of 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 120 and 126?

Solution: The factors of 120 and 126, respectively, are:

120 → 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

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

Hence, the greatest common factor of 120 and 126 is:

GCF (120, 126) = 6

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

What are the factors of 126?

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

What are the multiples of 126?

The first ten multiples of 126 = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260.

What is the prime factor form of 126?

The prime factor form of 126 is:

126 = 2 × 3 × 3 × 7 = 2 × 32 × 7

Is 126 a perfect square?

There is no perfect square for 126.

Is 126 a composite number or prime number?

The number 126 is composite.

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