A factor of 12 is a number that completely divides 12 without leaving a remainder. So the factors of 12 are 1, 2, 3, 4, 6, and 12. In this section, we will learn about the factors and prime factors of 12.
Also Read: Basic concepts of factors
Table of Contents
Highlights of Factors of 12
- 12=2×2×3. This is the prime factorization of 12.
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime factors of 12 are 2 and 3.
- Negative factors of 12 are –1, -2, -3, -4, -6, and –12.
What are the factors of 12?
Let us write the number 12 multiplicatively in all possible ways.
| 12 = 1×12 |
| 12 = 2×6 |
| 12 = 3×4 |
As there are no numbers between 3 and 4 that can divide 12, we will stop right now. So the factors of 12 are in pairs given as follows:
| 12 = a×b | Factors in Pairs (a,b) |
| 12 = 1×12 | (1, 12) |
| 12 = 2×6 | (2, 6) |
| 12 = 3×4 | (3,4) |
Thus the pair factors of 12 are (1, 12), (2, 6), and (3, 4). As all the numbers appearing in pair factors are the factors of 12, we conclude that the factors of 12 are 1, 2, 3, 4, 6, and 12.
As the factors of 12 are 1, 2, 3, 4, 6, and 12, we see that the total number of factors of 12 is six.
Prime Factors of 12
Note that the factors of 12 are 1, 2, 3, 4, 6, and 12. Among those factors, we notice that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 12 are 2 and 3.
Also Read:
| Factors of 8: | 1, 2, 4, 8 |
| Factors of 16: | 1, 2, 4, 8, 16 |
| Factors of 20: | 1, 2, 4, 5, 10, 20 |
| Factors of 24: | 1, 2, 3, 4, 6, 8, 12, 24 |
How to find factors of 12?
Now we will determine the factors of 12 by division method. In this method, we will try to find the numbers that can divide 12 with no remainder. See that
| 12/1=12 and the remainder is 0. | ∴ 1 and 12 are factors of 12. |
| 12/2=6 and the remainder is 0. | ∴ 2 and 6 are factors of 12. |
| 12/3=4 and the remainder is 0. | ∴ 3 and 4 are factors of 12. |
Note that no numbers other than the numbers in violet color can divide 12. So the numbers in violet color, that is, 1, 2, 3, 4, 6, and 12 are the complete list of factors of 12.
FAQs on Factors of 12
Ans: 1, 2, 3, 4, 6, and 12 are the factors of 12.
Ans: 2 and 3 are the prime factors of 12.
Ans: The prime factorization of 12 is 12=2×2×3.
Ans: The sum of factors of 12 are 1+2+3+4+6+12=28
This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.