The number 126 is an integer that can be factored into its prime factors to understand its composition better. Prime factorization of 126 reveals that it is the product of the prime numbers 2, 3, 3, and 7. These prime factors represent the fundamental building blocks of 126, highlighting its divisible components. Therefore, The factors of 126 consist of all possible combinations of these prime factors, including 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126. These factors represent the positive integers that can evenly divide 126 without leaving a remainder.
Furthermore, the Factors of the number126 can also be explored regarding their mathematical properties. For instance, the sum of all the factors (including 1 and 126) is 294, while the sum of the proper factors (excluding 1 and 126) is 168. The elements can also be paired up, so each pair of factors multiplies to give 126. Examples of such pairs include (1, 126), (2, 63), (3, 42), (6, 21), and (7, 18). These pairs highlight the concept of factor pairs, which are essential in understanding a number’s divisibility and prime factorization.
What are the Factors of 126?
A number’s factors are the numbers that divide it exactly, leaving no remainder. The Factors of the number126 are listed as 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126 in the definition of factors. As a result, 126 is a composite number since it has components besides 1 and itself. Let’s explore different ways to calculate the factors.
- Factors: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126
- Negative Factors: -1,-2,-3,-6,-7,-9,-14,-18,-21,-42,-63 and -126
- Prime Factors: 1,3,7
- Prime Factorization of 126: 2 x 3 x 3 x 7
- The Sum of Factors: 126
Key Points:
- The factors are 1, 2, 4, 31, 62, and 126.
- Six variables make up 126, which is more than most other numbers.
- 224, the sum of Factors of the number 126 is greater than 126. Therefore, 126 is a plentiful number.
- 2 x 2 x 31 is the prime factorization of 126.
- 4 is the biggest number that is a factor of both 126 and 36, making it the greatest common factor between the two numbers.
- Since 372 is the smallest number, a multiple of 126 and 36, it is the least common factor of these two numbers.
How to Calculate Factors of 126?
We can calculate Factors by following methods:
- Division Method
- Prime Factorization Method
- Factor Tree Methods
Pairs Factors of 126:
We must identify Factors of the number126 in pairs when multiplied together,. Both positive and negative factor pairs of 126 are possible.
| Positive Pair Factors | Negative Pair Factors |
| 1 × 126 | -1 × -126 |
| 2 × 63 | -2 × -63 |
| 3 × 42 | -3 × -42 |
| 6 × 21 | -6 × -21 |
| 7 × 18 | -7 × -18 |
| 9 × 14 | -9 × -14 |
Factors of 126 Using Division Method:
A factor evenly divides the original number. Therefore, we may determine its components by multiplying 126 by other natural integers.
| Division | Factor | Remainder |
| 126 ÷ 1 | 1 | 1 |
| 126 ÷ 2 | 2 | 1 |
| 126 ÷ 3 | 3 | 1 |
| 126 ÷ 6 | 6 | 1 |
| 126 ÷ 7 | 7 | 1 |
| 126 ÷ 9 | 9 | 1 |
| 126 ÷ 14 | 14 | 1 |
| 126 ÷ 18 | 18 | 1 |
| 126 ÷ 21 | 21 | 1 |
| 126 ÷ 42 | 42 | 1 |
| 126 ÷ 63 | 63 | 1 |
| 126 ÷ 126 | 126 | 1 |
What is the Prime Factorization of 126?
To find the prime factorization of 126, you can use the following steps:
- Begin by dividing 126 by the smallest prime number, which is 2.
126 ÷ 2 = 63
- Divide the resulting quotient, 63, by the smallest prime number again, 3.
63 ÷ 3 = 21
- Continue dividing the quotients by the smallest prime numbers until the quotient becomes 1.
21 ÷ 3 = 7
7 ÷ 7 = 1
- Write down the prime factors used in the divisions: 2, 3, 3, and 7.
- The prime factorization 126 is the product of these prime factors: 2 × 3 × 3 × 7.
Therefore, the prime factorization 126 is 2 × 3 × 3 × 7.
Factor Tree of 126
To create a factor tree for 126, follow these steps:
- Start by writing down the number 126.
- Find two Factors of the number126. The factors should multiply together to give 126. In this case, we can choose 6 and 21.
Continue factoring the numbers in the tree until all the branches lead to prime numbers. - The numbers at the bottom of the tree are prime factors.
- 2, 3, 3, and 7 are the prime Factors of the number 126.
The factor tree representation of 126 shows how the number can be factored into its prime components.
Examples: 1
What are the common factors of 182 and 126?
Solution:
The factors of 182 are 1, 2, 7, 13, 14, 26, 91, and 182. The Factors of the number126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126.
Therefore, the common factors of 182 and 126 are: 1, 2, 7, and 14.
Example: 2
Jim has 126 candies and wants to divide them evenly among 42 kids. Can you help Jim determine how many sweets each kid will receive?
Solution:
To divide 126 candies evenly among 42 kids, we need to perform the division: 126 ÷ 42 = 3.
Therefore, each kid will receive 3 candies.
No, 5 is not a factor of 126.
The prime factors 126 are 2, 3, and 7.
No, 10 is not a factor of 126.
The largest factor of 126 is 126 itself.
126 has a total of 12 factors.
