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.
Factors of 11: 1 and 11.
Prime Factorization of 11: 1 × 11 or 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:
Positive Factors of 11 | Positive Pair Factors of 11 |
1 × 11 | (1, 11) |
Negative Pair Factors of 11:
Negative Factors of 11 | Negative Pair Factors of 11 |
-1 × -11 | (-1, -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
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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:
- Determine the common factors of 11 and 9.
- Find the common factors of 11 and 22.
- Find the common factors of 11 and 7.
Frequently Asked Questions on Factors of 11
Q1
What are the factors of 11?
The factors of 11 are 1 and 11, as 11 is a prime number.
Q2
What is the prime factorization of 11?
The prime factorization of 11 is 1 × 11 or 11.
Q3
What are the positive and negative pair factors of 11?
The positive and negative pair factors of 11 are (1, 11) and (-1, -11), respectively.
Q4
Is 6 a factor of 11?
No, 6 is not a factor of 11. If 11 is divisible by 6, it leaves a remainder, and hence, 6 is not a factor of 11.
Q5
What is the sum of factors of 11?
The sum of factors of 11 is 12. We know that the factors of 11 are 1 and 11.
Hence, the sum of factors of 11 = 1+11 = 12.
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Now, let's break down the key concepts discussed in the article about the factors of 11:
Factors of 11:
In mathematics, factors are numbers that divide another number completely without leaving a remainder. For the prime number 11, its only factors are 1 and 11, both positive and negative: (1, 11, -1, -11).
Pair Factors of 11:
Pair factors are numbers multiplied together to result in the original number. Since 11 is a prime number, it has only one positive pair factor ((1 \times 11)) and one negative pair factor ((-1 \times -11)).
Positive Pair Factors of 11: (1 \times 11) Negative Pair Factors of 11: (-1 \times -11)
Division Method for Factors of 11:
The division method involves dividing 11 by different integers. Factors are the numbers for which the division yields a quotient without any remainder. In this case, the factors of 11 obtained through division are 1 and 11.
Prime Factorization of 11:
Prime factorization involves expressing a number as the product of its prime factors. Since 11 is a prime number, its prime factorization is simply (1 \times 11) or just (11).
Solved Examples:
The article provides examples demonstrating the application of factorization. For instance, finding common factors between 11 and other numbers (e.g., 10, 12, and 13) is illustrated.
Practice Problems:
Readers are encouraged to engage with practice problems to solidify their understanding of factors, including determining common factors and solving related mathematical queries.
FAQs:
Frequently asked questions provide concise answers to common queries about the factors of 11, prime factorization, positive and negative pair factors, and more.
In essence, this article comprehensively covers the factors of 11, employing various methods such as pair factorization, division, and prime factorization, supported by examples and practice problems to enhance the reader's grasp of these mathematical concepts.
