Definition of factors of 11: If a number completely divides 11 with the remainder zero, then that number is called a factor of 11.
Thus, we can say that the factors of 11 are the divisors of 11. In this section, we will learn about the factors of 11 and the prime factors of 11.
Also Read: Basic concepts of the factors of a number
Highlights of Factors of 11
- 11=1×11 is the prime factorization of 11.
- The factors of 11 are 1 and 11.
- The only prime factor of 11 is 11.
- Negative factors of 11 are –1 and –11.
What are the factors of 11?
To get the factors of 11 we need to first write the number 11 multiplicatively in all possible ways.
11 = 1×11
This is the only way we can express 11 multiplicatively. Therefore the factors of 11 in pairs are given as follows:
|11 = a×b||Factors in Pairs (a,b)|
|11 = 1×11||(1, 11)|
Thus the only pair factor of 11 is (1, 11). We know that all the numbers appearing in pair factors are the factors of 11. So we conclude that
The factors of 11 are:
1 and 11.
Number of Factors of 11
From above we have calculated the factors of 11 which are 1 and 11. Thus the total number of factors of 11 is two.
Prime Factors of 11
Note that the factors of 11 are 1 and 11. Among those factors, we observe that only 11 is a prime number as it does not have any proper divisors.
∴ the only prime factor of 11 is the number 11 itself.
Question: What are the factors of 11?
Video Solution: coming soon…
Is 11 a Prime Number?
As the factors of 11 are 1 and the number itself, by the definition of prime numbers, we can say that 11 is a prime number.
Conclusion: 11 is a prime number.
How to find factors of 11?
Now we will determine the factors of 11 by division method. In this method, we will find the numbers that can divide 11 with no remainder. See that
11/1=11 and the remainder is 0.
∴ 1 and 11 are factors of 11.
Note that no numbers other than the numbers in violet color can divide 11. So the numbers in violet color, that is, 1 and 11 are the complete list of factors of 11.