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Factors of 22: Prime Factorization, Methods, Tree, And, Examples
The factors of 22 are grouped as a set of natural numbers that produce zero as the remainder and a whole number quotient whenever they act as the divisors for the number 22. These numbers also give 22 as the product when they are multiplied together.
Figure 1 – All possible Factors of 22
What Are the Factors of 22?
The factors of 22 are 1, 2, 11, and 22. These numbers yield zero as the remainder when 22 is divided from them. In total, the number 22 has 4 factors. These factors are both positive as well as negative. These 4 factors can be grouped into 2-factor pairs. Moreover, the factor of 22 consists of 2 prime factors.How To Calculate the Factors of 22?
You can calculate the factors of 22 through two primary methods – the prime factorization method and the division method. Let’s first take a look at the division method.Division
There are 2 rules for a number to qualify as a factor when the division method is implied. The first rule is that the number must leave zero as the reminder and the second rule states that this number must also leave a whole number quotient.Before finding the factors of 22 through the division method, let’s first determine the range in which these factors lie. An easy way is to look for numbers between 1 and half of that number.Since half of 22 is 11, that means the range of factors of 22 must lie between 1 and the number 11. So we’ll check for all lying in this range to be qualified as a factor of 22. We also know that the number 22 is an even number so that automatically means that the number 2 will be a factor of 22. This is evident from the division shown below:\[ \frac{22}{2} = 11 \]As a whole number quotient is produced, this indicates that the number 2 is a factor of 22. Additional factors of the number 22 are shown below:\[ \frac{22}{1} = 22\]\[ \frac{22}{11} = 2 \]\[ \frac{22}{22} =1 \]Hence, the factor of 22 is given below:Factors of 22: 1, 2, 11, and 22These factors can be negative as well. There is no difference between positive and negative factors except for the sign. The positive factors have a positive (+) sign, and the negative factors have a negative (-) sign. The negative factors are given below:Negative Factors of 22: -1, -2, -11, and -22Factors of 22 by Prime Factorization
Prime factorization is the technique through which the prime factors of a number are determined. The factors of a number are both composite numbers and prime numbers. These prime numbers are known as prime factors.The division in prime factorization is carried out with the help of prime factors. The division begins with the number and undergoes division with a prime number. The whole number quotient produced acts as the next step’s dividend.This dividend then goes through the division with a prime number, and the same process is repeated. This process is continued until 1 is obtained at the end.The prime factorization of 22 is shown below:22 $\div$ 2 = 11
11 $\div$ 11 = 1
The prime factorization of 22 is also shown below in figure 1:
Figure 2 – Prime Factorization of 22
Factor Tree of 22
The factor tree is a visual representation of the prime factorization. It is also used to represent the prime factors of a number pictorially.The factor tree represents the prime factors of a number in a tree structure, due to which this process is known as a factor tree. The factor tree ends at prime numbers recognized as the prime factors.The factor tree begins with the number as the base and then extends two branches. One of the branches is directed towards a prime factor, and the other is directed towards the whole number quotient produced due to the division with the prime factor.The end branches of the factor tree only hold the prime factors. The factor tree for the number 22 is shown below in figure 2:
Figure 3 – Factor Tree of 22
Factors of 22 in Pairs
The factors of 22 can also be grouped in pairs known as the factor pairs. The factor pairs consist of two numbers, which, when multiplied together, produce the original number as a result.An easy way to determine the factor pairs is to group the number with its whole number quotient produced. For instance, take a look at the division shown below:\[ \frac{22}{2} = 11 \]When the number 2 acts as the divisor, the number 11 is produced as a whole number quotient. This categorizes 2 as a factor of 22. Moreover, the number 2 forms a factor pair with its respective whole number quotient produced as shown below:2 x 11 = 22
The factor pairs of the number 22 are shown below:1 x 22 = 22
2 x 11 = 22
Hence the factor pairs of 22 are given below:Factor Pairs of 22 = (1, 22) and (2, 11)These factor pairs can be negative as well. The requirement for negative factor pairs is that the number existing within the pair must have a negative sign to produce a positive product.The negative factor pairs of the number 22 are given below:-1 x -22 = 22
-2 x -11 = 22
Negative Factor Pairs of 22 = (-1, -22) and (-2, -11)So in total, the number 22 has 4 factors that can form 2 factor pairs. These factor pairs can be negative as well as positive.Factors of 22 Solved Examples
Some examples comprising the factors of 22 are given below to help you clear any ambiguity regarding factors 22.Example 1
Calculate the product of all the factors of 22 and the sum of all the factors of 22 and determine the difference between the two results.Solution
To solve this example, let’s first look at all the factors of 22. The factors of 22 are given below:Factors of 22: 1, 2, 11, and 22Now, let’s first calculate the product of these factors:Product of factors of 22 = 1 x 2 x 11 x 22
Product of factors of 22 = 484
So the product of the factors of 22 is 484.Now, let’s calculate the sum of the factors of 22. The sum is given below:Sum of factors of 22 = 1 + 2 + 11 + 22
Sum of factors of 22 = 36
So the sum of the factors of 22 is 36. Now, let’s calculate their difference.Difference = Product of factors of 22 – Sum of factors of 22
Difference = 484 – 36
Difference = 448
So the difference between the results of the product of the factors of 22 and the sum of the factors of 22 is 448.Example 2
Calculate the average of all the factors by 22.Solution
To calculate the average of all the factors 22, let’s first list them down. Factors of 22 are given below:Factors of 22 = 1, 2, 11, and 22The formula for average is given below:\[ Average = \frac{\text{Sum of all the factors}}{\text{Total number of factors}} \]\[ Average = \frac{1 + 2 + 11 + 22}{4} \]\[ Average = \frac{36}{4} \]Average = 9
So the average of all the factors of 22 is 9.Example 3
Calculate the product of the odd factors of 22 and determine if it’s a multiple.Solution
To calculate the product of odd factors of 22, let’s take a look at the list of the factors of 22.Factors of 22 = 1, 2, 11, 22The odd factors of 22 are given below:Odd Factors of 22 = 1, 11The product of odd factors of 22 is given below:Product of odd factors = 1 x 11
Product of odd factors = 11
The product of odd factors of 22 is 11. Since 11 is not an even number, that indicates that the number 11 is not a multiple of 2. All images/mathematical drawings are created with GeoGebra.