Factors of 12
The factors of 12 are the numbers that are multiplied in pairs, resulting in an original number. The pair factors of 12 can be positive or negative but it cannot be a decimal or fraction. For example, the pair factor of 12 can be (1, 12) or (-1, -12). The factors of a number can be found using the division method as well as the prime factorization method. In this article, we are going to learn the factors of 12, pair factors and the prime factors of 12 by prime factorization method with many examples.
Table of Contents:
- What are the Factors of 12?
- Pair Factors of 12
- Factors of 12 by Division Method
- Prime Factorization of 12
- Solved Examples
- FAQs
What are the Factors of 12?
The factors of 12 are the numbers that divide 12 exactly without leaving any remainder. As 12 is an even composite number, it has many factors other than 1 and 12. The factors of 12 can be positive or negative. Hence, the factors of 12 are 1, 2, 3, 4, 6 and 12. Similarly, the negative factors of 12 are -1, -2, -3, -4, -6 and -12.
Factors of 12: 1, 2, 3, 4, 6 and 12. Prime Factorization of 12: 2×2×3 or 2^{2} × 3 |
Pair Factors of 12
A pair of numbers that are multiplied together, resulting in an original number 12 is called the pair factor of 12. As discussed above, the pair factors of 12 can be positive or negative. The positive and negative pair factors of 12 are given below:
Positive Pair Factors of 12:
Positive Factors of 12 | Positive Pair Factors of 12 |
1 × 12 | (1, 12) |
2 × 6 | (2, 6) |
3 × 4 | (3, 4) |
Negative Pair Factors of 12:
Negative Factors of 12 | Negative Pair Factors of 12 |
-1 × -12 | (-1, -12) |
-2 × -6 | (-2, -6) |
-3 × -4 | (-3, -4) |
Factors of 12 by Division Method
In the division method, the factors of 12 can be found by dividing 12 by different integers. If the integer divides 12 and leaves the remainder 0, then those integers are the factors of 12. Now, let us discuss the factors of 12 by division method.
- 12/1 = 12 (Factor is 1 and remainder is 0)
- 12/2 = 6 (Factor is 2 and remainder is 0)
- 12/3 = 4 (Factor is 3 and remainder is 0)
- 12/4 = 3 (Factor is 4 and remainder is 0)
- 12/6 = 2 (Factor is 6 and remainder is 0)
- 12/12 =1 (Factor is 12 and remainder is 0)
Thus, the factors of 12 are 1, 2, 3, 4, 6 and 12. If the numbers other than 1, 2, 3, 4, 6 and 12 divide 12, 12 is not divided exactly and leaves the remainder.
Prime Factorization of 12
The prime factorization of 12 is the process of writing the number 12 as the product of its prime factors. The process to find the prime factors of 12 is given below:
Let us take the pair factor (1, 12)
Here, 1 is neither prime nor composite. So, leave the number as it is.
Now, take the other number in the pair factor (i.e. 12). We know that 12 is a composite number, and hence it can be further factored into its prime factors.
Thus, 12 can be written as the product of 2, 2 and 3, as both 2 and 3 are prime factors.
Hence, 12 = 2×2×3
Therefore, the prime factorization of 12 is 2×2×3 or 2^{2} × 3
Note:
If a number in the pair factor is a prime number, leave the number as it is. In case, if the number is composite, write the number as the product of its prime factors.
Examples
Example 1:
Find the common factors of 12 and 11.
Solution:
The factors of 12 are 1, 2, 3, 4, 6 and 12.
The factors of 11 are 1 and 11.
As 11 is a prime number, the common factor of 12 and 11 is 1.
Example 2:
Find the common factors of 12 and 13.
Solution:
Factors of 12 = 1, 2, 3, 4, 6 and 12.
Factors of 13 = 1 and 13.
Hence, the common factor of 12 and 13 is 1.
Example 3:
Find the common factors of 12 and 6.
Solution:
The factors of 12 are 1, 2, 3, 4, 6 and 12.
The factors of 6 are 1, 2, 3 and 6.
Hence, the common factors of 12 and 6 are 1, 2, 3 and 6.
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Frequently Asked Questions on Factors of 12
What are the factors of 12?
The factors of 12 are 1, 2, 3, 4, 6 and 12.
What is the prime factorization of 12?
The prime factorization of 12 is 2×2×3 or 2^{2} × 3.
Write down the positive pair factors of 12?
The positive pair factors of 12 are (1, 12), (2, 6) and (3, 4)
Write down the negative pair factors of 12?
The negative pair factors of 12 are (-1, -12), (-2, -6) and (-3, -4).
Is 6 a factor of 12?
Yes, 6 is a factor of 12. As 6 divides 12 exactly without leaving a remainder, 6 is a factor of 12.