Factors of 22 – With Division and Prime Factorization

Factors of 22

Factors Of 22

A factor of 22 is a number that divides it exactly, without leaving a remainder. It can also be a negative factor. 22 has both pair factors (2, 11) and (-2, 11). 

When we multiply the negative pair factors, such as multiplying -2 and -11, it leaves us with the original number 22. Factors of 22 cannot be decimals or fractions. 

Here, we will discuss what are the factors of 22, prime factors of 22, positive and negative pairs, and the two different methods we can use to find the factors of 22: First, we will discuss the division method, and then we will discuss the prime factorization method.

What are the Factors of 22?

A factor of 22 is the number that is multiplied in pairs to give the original number 22. In other words, the factors of 22 are the numbers that divide 22 exactly without leaving a remainder. 

Since 22 is an even composite number, it has more than two factors. In addition to itself and one other factor, 22 has several other factors. These factors are 1, 2, 11, and 22.

Factors of 22: 1, 2, 11 and 22

Prime Factorization of 22: 2 × 11 or 21 × 111

factors of 22

Pair Factors of 22

In mathematics, pair factors refer to those numbers which, when multiplied, give 22. It is possible to have a positive and a negative pair factor of 22. These are the positive and negative pair factors of 22.

Positive Pair Factor of 22:

Positive Factors of 22Positive Pair Factors of 22
1 × 22(1, 22)
2 × 11(2, 11)

Negative Pair Factor of 22:

Negative Factors of 22Negative Pair Factors of 22
-1 × -22(-1,-22)
-2 × -11(-2, -11)

Factors of 22 by Division Method

To find the factors of 22, divide the number 22 by the numbers 1, 2, 3, 4, 5, and so on, which leaves 0 as the remaining factor. 

It is necessary to start by dividing 22 by 1, and then by the next consecutive integer.

  • 22/1 = 22 
  • 22/2 = 11 
  • 22/11 = 2 
  • 22/22 = 1 

In the case of 22 divided differently from 1, 2, 11, and 22, the remainder value remains the same. 

Consequently, the factors of 22 are 1, 2, 11, and 22.

Prime Factorization of 22

In the prime factorization method, we will write the numbers as the product of their prime factors. Here’s how to find the prime factorization of 22.

Write down (1, 22) as the pair factor for 22

Check to see if the factors are composite or prime.

As long as both numbers are prime, multiply their prime factors.

When one of the numbers in the pair is a prime number and the other is a composite number, divide the composite number into its prime factors and multiply those factors together.

Multiply the prime factors of both composite numbers if they are both composites.

We will now learn how to find the prime factors of 22.

Take into account the pair factor (1, 22)

In this case, do not split the number 1 into further factors, as it cannot be separated.

There is another number 22, which you should take. It can be split further into its prime factors, such as 2 and 11, as well as a composite number.

Multiply the prime factors 1, 2, and 11 now.

In other words, 22 is the product of 1, 2, and 11.

Consequently, the prime factorization of 22 is 2 × 11 or 21 × 111

factor of 22 by prime factorization

Examples

Example 1:

What are the common factors of 22 and 11?

Solution:

1, 2, 11, and 22 are the factors of 22. 

Factors of 11 = 1 and 11.

Hence, 1 and 11 are the common factors of 11 and 22. 

Example 2:

Calculate the common factors between 22 and 20.

Solution:

Factors of 22 = 1, 2, 11 and 22.

1, 2, 4, 5, 10, and 20 are the factors of 20.

22 and 20 have the common factors of 1 and 2.

Example 3:

Find out what factors 22 and 44 have in common.

Solution:

22 has the factors 1, 2, 11, and 22.

Factors of 44 = 1, 2, 4, 11, 22, and 44.

1, 2, 11, and 22 are the common factors of 22 and 44.

Factors of 12

FAQs

How many factors does 22 have??

22 has more than two factors since it is a composite number. 1, 2, 11, and 22 are the factors of 22.

In what way is 22 prime factorized?

Prime factorization of 22 =  2 × 11.

What are the positive and negative pair factors of 22?

Positive pair factors of 22 = (1, 22) and (2, 11)

(-1, -22) and (-2, -11) are the negative pair factors of 22.

4 a factor of 22; is it true?

No, 4 cannot be divided by 22. By dividing 22 by 4, we get 2 as the remainder, so 4 is not a factor of 22.

Factors of 42=1, 2, 3, 6, 7, 14, 21, and 42.Factors of 48=1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Factors of 64=1, 2, 4, 8, 16, 32, 64Factors of 96= 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96.

Leave your vote