Factors of 11—with division and prime factorization

Factors of 11

Factors of 11

Factors of 11 are numbers that divide 11 completely and leave 0 as a remainder. 

It is possible to express 11 factors in both positive and negative forms. Similarly, the pair factor of 11 can be expressed as a positive or negative number. 

For example: 

The original number is 11 if you multiply -1 by -11. 

Using the prime factorization method, we will discover the positive and negative pair factors of 11 as well as prime factors of 11.

What are the Factors of 11?

Factors of 11 are the numbers that divide 11 completely without leaving any remainder. Therefore, the factors of 11 are the numbers multiplied in pairs, resulting in the original number 11. Since 11 is a prime number, it has only two factors: one and the number itself. Thus, the factors of 11 are 1 and 11, and the negative factors of 11 are -1 and -11.

Factors of 11
Factors of 11: 1 and 11.Prime Factorization of 11: 1 × 11 or 11

What are Factors of -11?

When we multiply two numbers, and we get -11 as a product, that numbers are the factors of -11. Here is the explanation:

-1 × 11 = -11

 1 × -11 = -11

We can get -11 by having (-1, 11) as a pair of factors. Similarly, we can also get -11 by having (1, -11)as a pair of factors.

Pair Factors of 11

It is known as the pair factor of 11 when two numbers are multiplied together in pairs. 11 has one positive pair factor and one negative pair factor, since it is a prime number. Let us see what those factors are.

Positive Pair Factors of 11:

Positive Factors of 11Positive Pair Factors of 11
1 × 11(1, 11)

Negative Pair Factors of 11:

Negative Factors of 11Negative Pair Factors of 11
-1 × -11(-1, -11)

Therefore, the positive and negative pair factors of 11 are (1, 11) and (-1, -11), respectively.

Factors of 11 by Division Method

Using the division method, the factors of 11 are determined by dividing 11 by different integers. When the integer numbers divide 11 exactly, then those integers are the factors of 11. 

Here are the factors of 11:

11/1 = 11 (Factor is 1 and Remainder is 0)

11/11 = 1 (Factor is 11 and Remainder is 0)

Dividing 11 by any number other than 1 or 11 leaves a remainder of some value. Therefore, the factors of 11 are 1 and 11.

Prime Factorization of 11

The number 11 is written as the product of its prime factors in the prime factorization of 11. 

Here you will know how to find the prime factors of 11:

Let’s say (1, 11) is the pair factor.

In other words, number 1 cannot be factored further because it is neither prime nor composite.

Let’s take the other prime number, 11, as well.

As a result, write 11 as the product of 1 and 11.

Thus, the prime factorization of 11 is 1 × 11 or 11.

Learn More Factors of a Number:

Factors of 12= 1, 2, 3, 4, 6, and 12.Factors of 17= 1 and 17.
Factors of 23= 1, 23.Factors of 24=  1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.Factors of 49= 1, 7, 49.

Solved Examples

Example 1:

Calculate the common factor of 11 and 10.

Solution:

The factors of 11 are 1 and 11.

The factors of 10 are 1, 2, 5, and 10.

The common factor of 11 and 10 is 1, since 11 is a prime number.

Example 2:

Find out the common factor of 11 and 12.

Solution:

Factors of 11 = 1 and 11.

Factors of 12 = 1, 2, 3, 4, 6 and 12.

As 11 is a prime number, it is the common factor of 11 and 12.

Example 3:

Calculate the common factor of 11 and 13.

Solution:

The factors of 11 are 1 and 11.

The factors of 13 are 1 and 13.

The common factor of 11 and 13 is 1 because they are both prime numbers.

Practice Problems

Here are the problems to solve:

Calculate the common factors between 11 and 9.

Calculate the common factor of 11 and 22.

Finding the common factor between 11 and 7 is easy.

Factors of 23

FAQ’s

What are the factors of 11?

 As 11 is a prime number. The factors of 11 are 1 and 11,

What is the prime factorization of 11?

Prime factorization of 11 = 1 × 11 or 11.

What are the positive and negative pair factors of 11?

(1, 11) and (-1, -11) are the positive and negative pair factors of 11.

Is 6 a factor of 11?

No, 6 is not a factor of 11. As 11 is divisible by 6, it leaves a remainder, so 6 cannot be a factor of 11.

What is the sum of factors of 11?

The sum of the factors of 11 is 12. 1 and 11 are the factors of 11.

Therefore, the sum of factors of 11 = 1+11 = 12.

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