Definition of factors of 3: If a number completely divides 3 with the remainder zero, then that number is called a factor of 3.
By the above definition, we can say that the factors of 3 are the divisors of 3. In this section, we will learn about the factors of 3 and the prime factors of 3.
Also Read: Basic concepts of factors
Highlights of Factors of 3
- 3=1×3 is the prime factorization of 3.
- The factors of 3 are 1 and 3.
- The only prime factor of 3 is 3.
- Negative factors of 3 are –1 and –3.
What are the Factors of 3?
To get the factors of 3 we need to first write the number 3 multiplicatively in all possible ways. Note that we have:
3 = 1×3
This is the only way we can express 3 multiplicatively. Therefore the factors of 3 in pairs are given as follows:
| 3 = a×b | Factors in Pairs (a,b) |
| 3 = 1×3 | (1, 3) |
Thus the only pair factor of 3 is (1, 3). We know that all the numbers appearing in pair factors are the factors of 3. So we conclude that
|
The factors of 3 are: 1 and 3. |
Number of Factors of 3
From above we have calculated the factors of 3 which are 1 and 3. Thus the total number of factors of 3 is two.
Prime Factors of 3
Note that the factors of 3 are 1 and 3. Among those factors, we observe that only 3 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 3 is the number 3 itself.
Question: What are the factors of 3?
Video Solution:
Is 3 a Prime Number?
As the factors of 3 are 1 and the number 3 itself, by the definition of prime numbers, we can say that 3 is a prime number.
Conclusion: 3 is a prime number.
How to Find Factors of 3?
Now we will determine the factors of 3 by division method. In this method, we will find the numbers that can divide 3 with no remainder. See that
| 3/1=3 and the remainder is 0. | ∴ 1 and 3 are factors of 3. |
Note that no numbers other than the numbers in violet color can divide 3. So the numbers in violet color, that is, 1 and 3 are the complete list of factors of 3.