Factors of 22 Using Prime Factorization
What are the Factors of 22?
A factor of a number is an integer that divides the number evenly, that is, leaves no remainder. The factors of a number can be determined using divisibility rules and division facts. Here, we will learn about the factors, prime factors, and factor pairs of 22.
The factors of 22 are those integers that divide 22 without leaving any remainder. In other words, the factors of 22 will divide it evenly.
The factors of 22 can be positive as well as negative, but they cannot be decimals or fractions. The quotient obtained by dividing 22 by its factor is also a factor of 22.
The Factors of 22
Factors | Factor Pair | Prime factorization |
|---|---|---|
1, 2, 11, 22 | (1, 22), (2, 11) | 22 = 2 x 11 |
For example, 2 is a factor of 22 because on dividing 22 by 2, we get 0 as the remainder and 11 as the quotient, which is also a factor of 22.
Factor List for Number 22
Divisor | Is the number a factor of 22? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 22 = 22 |
2 | Yes, 22 is even. | 2 x 11 = 22 |
3 | No, 2 + 2 = 4, 22 is not divisible by 3 | - |
4 | No, 22 ÷ 4 = 5 Remainder = 2 | - |
5 | No, the ones digit is 2 | - |
6 | No, 22 ÷ 6 = 3 Remainder = 4 | - |
7 | No, 22 ÷ 7 = 3 Remainder = 1 | - |
8 | No, 22 is odd. | - |
9 | No, 22 ÷ 9 = 2 Remainder = 4 | - |
10 | No, the ones digit is not 0 | - |
11 | Yes, 22 ÷ 11 = 2 | 11 x 2 = 22 |
Therefore, the factors of 22 are 1, 2, 11, and 22.
The Prime Factors of 22
A factor tree can be used to determine the prime factors of 22, as shown in the figure.
From the factor tree, we can see that the prime factorization of 22 is 2 x 11.
This means that 2 and 11 are the prime factors of 22.
Read More:
The Factor Pairs of 22
The factor pair of any number is a set of two integers that, when multiplied, results in that number. So, these two integers are the factors of the number. A factor pair can be negative or positive.
[Note: The product of two negative numbers is positive.]
The factor pair of 22 is the set of two factors of 22 which, when multiplied, give 22 as the product.
Thus, the factor pairs of 22 can be obtained from the list of its factors.
Positive factors of 22 | Positive factor pair of 22 |
|---|---|
1 x 22 | (1, 22) |
2 x 11 | (2, 11) |
Solved Factors of 22 Examples
Example 1: Jennifer has a collection of 22 books on the geography and history of Europe. The books are to be arranged evenly on 2 shelves. How many books will she place on each shelf?
Solution:
22 books are to be evenly arranged on 2 shelves.
To find out how many books can be placed on each shelf, we will divide 22 by 2, that is,
\(\frac{22}{2}\)
= \(\frac{11 \times 2}{2}\) [(2, 11) is a factor pair of 22]
= 11 [Divide both the numerator and the denominator by 2]
Hence, Jennifer can place 11 books on each shelf.
Example 2: Find the common factors of 135 and 22.
Solution:
The factors of 135: 1, 3, 5, 9, 15, 27, 45, and 135
The factors of 22: 1, 2, 11, and 22
So, the common factor of 22 and 135 is 1.
Hence, 135 and 22 have only one common factor.
Example 3: What are the common factors of 22 and 168?
Solution:
The factors of 22 are 1, 2, 11, and 22
The Factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, and 168.
So, the common factors of 22 and 168 are 1 and 2.
No, 5 is not a factor of 22 as the number 5 does not divide 22 exactly. It leaves the remainder 2. So, 5 is not a factor of 22.
Yes, 22 is a composite number as it has factors other than 1 and itself, that is, 22. In other words, the number 22 has more than two factors.
The factors of 22 are 1, 2, 11, and 22
So, the smallest factor of 22 is 1 and the greatest factor is 22 itself.
The factors of 22 are 1, 2, 11, and 22
Hence, the sum of all the factors of 22 is
= 1 + 2 + 11 + 22
= 36
Hence, the sum is 36.
The factors of 22: 1, 2, 11, and 22. So, there are four factors of 22.