Factors of 11

The factors of 11 are the numbers that divide 11 completely and leave a remainder 0. The factors of 11 can be expressed in positive form as well as in negative form. Similarly, the pair factor of 11 can be represented using the positive and negative form. For example, multiplying -1 and -11 results in the original number 11. In this article, we are going to learn the factors of 11, positive and negative pair factors of 11, prime factors of 11 using the prime factorization method and many solved examples.

Table of Contents:

• What are the Factors of 11?
• Pair Factors of 11
• Factors of 11 by Division Method
• Prime Factorization of 11
• Solved Examples
• Practice Problems
• FAQs

What are the Factors of 11?

In Mathematics, the numbers that divide 11 completely without leaving any remainder are the factors of 11. In other words, the factors of 11 are the numbers that are multiplied in pairs and resulting in the original number 11. As 11 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 11 are 1 and 11, and the negative factors of 11 are -1 and -11.

Pair Factors of 11

The numbers multiplied together in pairs, resulting in 11, is called the pair factor of 11. As 11 is a prime number, it has one positive pair factor and one negative pair factor. The following are the positive and negative pair factors of 11.

Positive Pair Factors of 11:

Negative Pair Factors of 11:

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

Factors of 11 by Division Method

In the division method, the factors of 11 are found by dividing 11 by different integer numbers. If the integer numbers divide 11 exactly, then those integers are the factors of 11. The following 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)

If any numbers other than 1 and 11 divide 11, it leaves a remainder of some value. Hence, the factors of 11 are 1 and 11.

Prime Factorization of 11

In the prime factorization of 11, the number 11 is written in the form of the product of its prime factors. The prime factors of 11 can be found as follows:

Take the pair factor of 11, say (1, 11).

We know that the number 1 is neither prime nor composite, and hence, it cannot be factored further.

So, take the other factor, 11, which is also a prime number.

Hence, write the number 11 as the product of 1 and 11.

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

Video Lesson on Prime Factors

Solved Examples

Example 1:

Find 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.

As 11 is a prime number, the common factor of 11 and 10 is 1.

Example 2:

Find the common factor of 11 and 12.

Solution:

Factors of 11 = 1 and 11.

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

The common factor of 11 and 12 is 1, as 11 is a prime number.

Example 3:

Find the common factor of 11 and 13.

Solution:

The factors of 11 are 1 and 11.

The factors of 13 are 1 and 13.

As both the numbers 11 and 13 are prime numbers, the common factor of 11 and 13 is 1.

Practice Problems

Solve the following problems:

1. Determine the common factors of 11 and 9.
2. Find the common factors of 11 and 22.
3. Find the common factors of 11 and 7.