Definition of factors of 6: If a number completely divides 6 without a remainder, then that number is called a factor of 6.
By the above definition, we can say that the factors of 6 are the divisors of 6. In this section, we will learn about the factors of 6 and the prime factors of 6.
Also Read: Basic concepts of the factors of a number
Highlights of Factors of 6
- 6=2×3 is the prime factorization of 6.
- The factors of 6 are 1, 2, 3, and 6.
- Prime factors of 6 are 2 and 3.
- Negative factors of 6 are –1, -2, -3, and –6.
What are the Factors of 6?
Let us write the number 6 multiplicatively in all possible ways. We have:
6 = 1×6
6 = 2×3
As we can express 6 multiplicatively in no other ways, so we will stop right now. So the factors of 6 in pairs are given as follows:
| 6 = a×b | Factors in Pairs (a,b) |
| 6 = 1×6 | (1, 6) |
| 6 = 2×3 | (2, 3) |
Thus the pair factors of 6 are (1, 6) and (2, 3). As all the numbers appearing in pair factors are the factors of 6, we conclude that
|
The factors of 6 are: 1, 2, 3, and 6. |
Number of factors of 6
From above we have calculated the factors of 6 which are 1, 2, 3, and 6. Thus the total number of factors of 6 is four.
Prime Factors of 6
Note that the factors of 6 are 1, 2, 3, and 6. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.
∴ the prime factors of 6 are 2 and 3.
Question: What are the factors of 6?
Video Solution:
How to find factors of 6?
Now we will determine the factors of 6 by division method. In this method, we will find the numbers that can divide 6 with no remainder. See that
6/1=6 and the remainder is 0.
∴ 1 and 6 are factors of 6.
6/2=3 and the remainder is 0.
∴ 2 and 3 are factors of 6.
Note that no numbers other than the numbers in violet color can divide 6. So the numbers in violet color, that is, 1, 2, 3, and 6 are the complete list of factors of 6.
