Factors of 6
Factors are the numbers, that can divide the original number, evenly. Also, when two integers are multiplied together to get 6 as a result, then they are called pair factors of the produced number. Consider an example, the factor pairs of 6 are written as (1, 6) and (-1, –6). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × –6, then we get the number 6. Thus, we can consider both positive and negative factor pairs of 6. Factor pairs of the number 6 are the whole numbers which could be either positive or negative but not a fraction or decimal number.
To find the factors of a number, 6, we will use the factorization method. In the factorization method, first take the numbers, 1 and 6 as factors of 6 and proceed with finding the other pair of multiples of 6 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 6 in pairs and also the division method to find the prime factors of 6 is discussed.
Table of Contents:
- What are the Factors of 6?
- Pair Factors of 6
- Factors of 6 by Division Method
- Prime Factorization of 6
- Solved Examples
- FAQs
What are the Factors of 6?
The factors of 6 are the numbers that divide 6 exactly without leaving the remainder. In other words, the factors of 6 are the numbers that are multiplied in pairs resulting in an original number 6. As 6 is an even composite number, it has many factors other than 1 and 6. Thus, the factors of 6 are 1, 2, 3 and 6. Similarly, the negative pair factors of 6 are -1, -2, -3 and -6.
Factors of 6: 1, 2, 3 and 6. Prime Factorization of 6: 2 × 3 or 2^{1} × 3^{1}. |
Pair Factors of 6
To find the pair factors of 6, multiply the two numbers in a pair to get the original number as 6, such numbers are as follows:
numbers are as follows:
Positive Pair Factors of 6:
Positive Factors of 6 |
Positive Pair Factors of 6 |
1 × 6 |
(1, 6) |
2 × 3 |
(2, 3) |
Therefore, the positive pair factors of 6 are (1, 6), and (2, 3).
Similarly, the negative pair factors of 6 are given below:
Negative Pair Factors of 6:
Negative Factors of 6 |
Negative Pair Factors of 6 |
-1 × -6 |
(-1, -6) |
-2 × -3 |
(-2, -3) |
Therefore, the negative pair factors of 6 are (-1, -6), and (-2,- 3).
Factors of 6 by Division Method
In the division method, the factors of 6 can be found by dividing 6 by different integers. If the integers divide 6 exactly and leave the remainder 0, then those integers are the factors of 6. Now, let us discuss how to find the factors of 6 using the division method.
- 6/1 = 6 (Factor is 1 and Remainder is 0)
- 6/2 = 3 (Factor is 2 and Remainder is 0)
- 6/3 = 2 (Factor is 3 and Remainder is 0)
- 6/6 = 1 (Factor is 6 and Remainder is 0)
If we divide the number 6 by any numbers other than 1, 2, 3 and 6, then it leaves the remainder. Hence, the factors of 6 are 1, 2, 3 and 6.
Prime Factorization of 6
The number 6 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 6.
Step 1: The first step is to divide the number 6 with the smallest prime factor, say 2.
6 ÷ 2 = 3
Step 2: Again if you divide 3 by 2, you will get a fractional value. So proceed with the next prime number say 3.
3 ÷ 3 = 1
Finally, you received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 6 are written as 2 × 3, where 2 and 3 are prime numbers.
It is possible to find the exact number of factors with the help of prime factorisation. The prime factor of the 6 is 2 x 3. The exponent in the prime factorisation is 1 and 1. When you add the number 1 with the exponent, it becomes (1+1)(1+1) = 2 x 2 =4. Therefore, the number 6 has 4 factors.
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Examples
Example 1:
Find the common factors of 6 and 5.
Solution:
The factors of 6 are 1, 2, 3 and 6.
The factors of 5 are 1 and 5.
As 5 is a prime number, the common factor of 6 and 5 is 1.
Example 2:
Find the common factors of 6 and 7.
Solution:
Factors of 6 = 1, 2, 3 and 6.
Factors of 7 = 1 and 7.
The common factor of 6 and 7 is 1 only since 7 is a prime number.
Example 3:
Find the common factors of 6 and 12.
Solution:
The factors of 6 are 1, 2, 3 and 6.
The factors of 12 are 1, 2, 3, 4, 6 and 12.
Hence, the common factors of 6 and 12 are 1, 2, 3 and 6.
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Frequently Asked Questions on Factors of 6
What are the factors of 6?
The factors of 6 are 1, 2, 3 and 6.
What is the prime factorization of 6?
The prime factorization of 6 is 2 × 3.
What are the positive and negative pair factors of 6?
The positive pair factors of 6 are (1, 6) and (2, 3)
The negative pair factors of 6 are (-1, -6) and (-2, -3).
What is the sum of factors of 6?
The sum of factors of 6 is 12. We know that the factors of 6 are 1, 2, 3 and 6.
Hence, the sum of factors of 6 is 1+2+3+6 is 12.
Is 3 a factor of 6?
Yes, 3 is a factor of 6. If 6 is divisible by 3, it leaves a remainder zero, and hence 3 is a factor of 6.