The numbers that can divide an original number evenly are called factors also, when two integers are multiplied and produce the number 6. As a result, they are called the pair factors of 6. For example, These are represented by the symbols (1, 6) and (-1, -6). The original number should be produced when we multiply negative elements. For example, if we multiply -1 by -6, we get 6. As a result, we can consider both positive and negative pairs. The whole numbers that makeup factor pairs for the number 6 can be positive or negative, but they cannot be a fraction or a decimal number.
We will use the factorization method to discover the factors of the number 6. In the factorization method, the numbers 1 and 6 are considered factors. Then, the other pair of multiples of 6 are found, and the result is returned as an original number. Read the article below to find factor 6 in pairs and the division method to find the prime factors of number 6 to comprehend this strategy better.
What are the Factors of 6?
These are the numbers that divide evenly into 6 without leaving a remainder.
- Factors of 6: 1, 2, 3 and 6
- Negative Factors: -1, -2, -3 and -6
- Prime Factors: 2, 3
- Prime Factorization of 6: 2 × 3 = 2 × 3
- The sum of Factors: 12
To determine, you can find all the numbers that divide 6 without a remainder. Starting with 1, you check if it divides 6 evenly, which it does. Then you move to the next number, 2, and check if it divides 6 evenly. Again, it does. Next, you check 3, which is also its factor. Finally, you check 6 itself, and it also divides evenly. Therefore, the factors are 1, 2, 3, and 6.
Key Points:
- 1, 2, 3, and 6 are the factors of six.
- A universal factor is 1. It affects all numbers as a factor.
- Since it divides itself exactly, the number is a factor of itself.
- The factors of number 6 are (2, 3), (3, 2), (6, 1), and (1, 6), all of which are pairs.
- The 6 has prime factors 2 and 3.
Pair Factors of 6
The number 6 has many pairs of factors. Factors are numbers that can divide another number evenly without leaving a remainder.
Positive Pair Factors of number 6:
| Positive Factors | Positive Pair Factors |
| 1 × 6 | (1, 6) |
| 2 × 3 | (2, 3) |
Negative Pair Factors of number 6:
| Negative Factors | Negative Pair Factors |
| -1 × -6 | (-1, -6) |
| -2 × -3 | (-2, -3) |
Number 6 Factors by Division Method
By dividing 6 by various integers, the division method can be used to determine. The integers are also its factors if they divide 6 perfectly, leaving 0 as the remainder. Let’s now discuss how to divide a number by six to determine its factors.
| Division | Factor | Remainder |
| 6 ÷ 1 | 1 | 0 |
| 6 ÷ 2 | 3 | 0 |
| 6 ÷ 3 | 2 | 0 |
| 6 ÷ 6 | 1 | 0 |
Prime Factorization of 6
To find the prime factorization of 6, you can follow these steps:
- Start with the number 6.
- Check if it is divisible by the smallest prime number, 2. In this case, 6 is divisible by 2.
- Divide 6 by 2: 6 ÷ 2 = 3.
- Now, you have the quotient 3.
- Check if 3 is divisible by any prime numbers greater than 2. In this case, 3 is only divisible by itself.
- The factorization is complete when you have expressed the number as a product of prime numbers. In this case, 6 = 2 × 3.
- Therefore, the prime factorization of 6 is 2 × 3.
How to find Factor Tree of 6:
To find the factor tree of 6, you can follow these steps:
Start with the number 6.
- Think of two numbers that multiply together to give 6. In this case, 2 and 3 are the factors of 6.
- Write 6 at the top of the paper or board.
Draw two branches below 6, and write 2 on one branch and 3 on the other.
- The branch with 2 represents one factor.
- The branch with 3 represents the other factor of 6.
Check if the factors can be further broken down into smaller prime numbers.
- Since 2 is a prime number, you can’t break it down further.
- However, 3 is already a prime number.
The factor tree is complete when all the branches end with prime numbers.
In this case, the factor tree of 6 is as follows:
Example 1:
Find the common factors of 18 and 6.
Solution:
To find the common factors of 18 and 6, we need to determine the factors of both numbers and identify the factors that are common to both.
The factors are 1, 2, 3, and 6. The factors of 18 are 1, 2, 3, 6, 9, and 18.
By comparing the factors of both numbers, we can identify the factors common to both 6 and 18. In this case, the common factors are 1, 2, 3, and 6.
Therefore, the common factors of 18 and 6 are 1, 2, 3, and 6.
Example 2:
What are the common factors between -6 and 38?
Solution:
The common factors of two numbers are the positive integers that divide both numbers evenly. In the case of -6 and 38, we need to consider the absolute values of the numbers to find the common factors.
The absolute value of -6 is 6, and the factors are 1, 2, 3, and 6. The factors of 38 are 1, 2, 19, and 38.
Therefore, the common factors of -6 and 38 are 1 and 2.
The number 6 has 4 factors.
To find the factors, we list all the numbers that divide 6 without leaving a remainder. The factors of number 6 are 1, 2, 3, and 6.
The largest factor of the number 6 is 6.
