The factors of 22 are the numbers that divide the number 22 exactly without leaving the remainder. The factors of 22 can be positive as well as negative. For example, the pair factors of 22 can be (2, 11) as well as (-2, -11). If we multiply the negative pair factors, such as multiplying -2 and -11, it results in the original number 22. The factors of 22 can neither be decimal nor fraction. In this article, we are going to discuss what are the factors of 22, prime factors of 22, positive and negative pairs and the two different methods such as the division method and the prime factorization methods for finding the factors of 22.
Table of Contents:
- What are the Factors of 22?
- Pair Factors of 22
- Factors of 22 by Division Method
- Prime Factorization of 22
- Solved Examples
- FAQs
What are the Factors of 22?
The factors of 22 are the numbers, which are multiplied in pairs resulting in the original number 22. In other words, the factors of 22 are the numbers that divide the number 22 exactly without leaving the remainder. As the number 22 is an even composite number, it has more than two factors. The factors of 22 have more factors other than one and the number itself. The factors of 22 are 1, 2, 11 and 22.
Factors of 22: 1, 2, 11 and 22 Prime Factorization of 22: 2 × 11 or 2^{1} × 11^{1} |
Pair Factors of 22
The pair factors of 22 are the pair of numbers, which on multiplication gives the number 22. The pair factors of 22 can be a positive pair as well as a negative pair. The following are the positive pair factors and negative pair factors of 22.
Positive Pair Factor of 22:
Positive Factors of 22 |
Positive Pair Factors of 22 |
1 × 22 |
(1, 22) |
2 × 11 |
(2, 11) |
Negative Pair Factor of 22:
Negative Factors of 22 |
Negative Pair Factors of 22 |
-1 × -22 |
(-1,-22) |
-2 × -11 |
(-2, -11) |
Factors of 22 by Division Method
In the division method, the factors of 22 can be found by dividing the number 22 by numbers 1, 2, 3, 4, 5, and so on, which leaves the remainder 0. First, we have to start dividing 22 by 1, and then divide 22 by the next consecutive integers.
- 22/1 = 22 (Factor = 1 and remainder = 0)
- 22/2 = 11 (Factor = 2 and remainder = 0)
- 22/11 = 2 (Factor = 11 and remainder = 0)
- 22/22 = 1 (Factor = 22 and remainder = 0)
If we divide the number 22 other than 1, 2, 11 and 22, it leaves the remainder value. Hence, the factors of 22 are 1, 2, 11 and 22.
Also, read: |
Prime Factorization of 22
The prime factorization of 22 is the process of writing the numbers as the product of its prime factors. The prime factorization of 22 can be found as follows.
Step 1: Write down the pair factor of 22, say (1, 22)
Step 2: Check whether the factors are prime or composite.
If both the numbers are prime, multiply the prime factors as it is.
If one of the numbers in the pair is a prime number, and the other number is composite, split the composite number into its prime factors, and multiply the prime factors.
If both the numbers are composite, split both the composite numbers into their prime factors and multiply the prime factors.
Let us learn how to find the prime factors of 22.
Consider the pair factor (1, 22)
Here, leave the number 1, as it cannot be split into further factors.
Take the other number 22. The number 22 is a composite number and it can be split further as the product of its prime factors, such as 2 and 11.
Now, multiply the prime factors such as 1, 2, and 11
Therefore, 22 can be written as the product of 1, 2 and 11.
Thus, the prime factorization of 22 is 2 × 11 or 2^{1} × 11^{1}
Examples
Example 1:
Find the common factors of 22 and 11.
Solution:
The factors of 22 are 1, 2, 11 and 22.
The factors of 11 are 1 and 11.
Thus, the common factors of 22 and 11 are 1 and 11.
Example 2:
Find the common factors of 22 and 20.
Solution:
Factors of 22 = 1, 2, 11 and 22.
Factors of 20 = 1, 2, 4, 5, 10 and 20
The common factors of 22 and 20 are 1 and 2.
Example 3:
Find the common factors of 22 and 44.
Solution:
The factors of 22 are 1, 2, 11 and 22.
The factors of 44 are 1, 2, 4, 11, 22 and 44.
The common factors of 22 and 44 are 1, 2, 11 and 22.
Frequently Asked Questions on Factors of 22
What are the factors of 22?
The factors of 22 are 1, 2, 11 and 22. As the number 22 is a composite number, it has more than two factors.
What is the prime factorization of 22?
The prime factorization of 22 is 2 × 11.
Write down the positive and negative pair factors of 22.
The positive pair factors of 22 are (1, 22) and (2, 11)
The negative pair factors of 22 are (-1, -22) and (-2, -11).
How to find the factors of 22 by division method?
The factors of 22 using the division method as follows:
22/1 = 22 ( Factor is 1)
22/2 = 11 (Factor is 2)
22/11 = 2 (Factor is 11)
22/22 = 1 (Factor is 22)
Thus, the factors of 22 are 1, 2, 11 and 22.
Is 4 a factor of 22?
No, 4 is not a factor of 22. If we divide 22 by 4, it leaves the remainder 2 and hence 4 is not a factor of 22.