banner

Factors of 162: Prime Factorization, Methods, Tree, and Examples

The factors of 162 are the numbers that divide it entirely and evenly. These numbers always exist within the range of factors of 162, which is calculated by dividing 162 by 2. 

This makes the factorization processes easier. These processes are the division method, Prime factorization, and factor tree diagram. We will study these in detail in this article.

What Are the Factors of 162?

The factors of 162 are the following: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162. 

162 is an even number. It is also a composite number with ten factors, which means that it is not a prime number; hence it has more than two factors.

How To Calculate the Factors of 162?

The factors of 162 are calculated using the primary division method by drawing a factor tree diagram and performing prime factorization. In this part, we will learn about the division method used for finding the factors of 162.

In the division method, we divide 162 by all possible numbers within its factor range to find out its factors. A factor is identified if it divides 162 evenly or completely.

\[ \frac{162}{ 2} = 81 \]

\[ \frac{162}{ 3} = 54\]

\[ \frac{162}{ 6 }= 27 \]

\[ \frac{162}{ 9} = 18 \]

\[ \frac{162}{ 18} = 9 \]

\[ \frac{162}{ 27} = 6 \]

\[ \frac{162 }{ 54} = 3\]

\[ \frac{162}{ 81} = 2 \]

\[ \frac{162}{ 162}  = 1\]

\[ \frac{162}{ 1 }= 162 \]

All the divisors shown in this division give a whole number quotient, hence they are the factors of 162. The factors of 162 are:

Factors of 162 through division method: 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162

Factors of 162 by Prime Factorization

Prime factorization of 162 is a technique that gives us only the prime factors of 162. In this method, we divide 162 only by prime numbers. Now we already know that prime numbers can be defined as numbers that are only utterly divisible by themselves, and 1 is a universal factor. 

We can find such numbers through prime factorization, which gives us 162 when multiplied together. This method for 162 has been shown in detail here.

The first task is to write down the number and check whether it is even or odd; if it is an even number, we start by using 2 as the divisor, but if it is odd, we check with other prime numbers. 162 is an even number, so it is divisible by 2:

162 $\div$ 2 = 81

In the next step, we will use 81 as the dividend. Now 81 is divisible by 3, so:

81 $\div$ 3 = 27

We will now use 27 as the dividend for this step. 27 is again divisible by 3, so we will not look for any other prime number:

27 $\div$ 3 = 9

9 is also divisible by 3:

9 $\div$ 3 = 3

3 $\div$ 3 = 1

This marks the end of prime factorization because 3 / 3 = 1, and we have gotten our final answer equivalent to 1. 

We will now pick up and write down all the divisors in each step because these are the prime factors of 162. 2 and 3 are the prime factors of 162.

Using an equation, this can be written as:

Prime factorization of 162 = 2 x 3 x 3 x 3 x 3

The prime factorization is also shown below:

Figure 2

Factor Tree of 162

The factor tree of 162 is a diagram that can visually express the entire prime factorization technique. It is drawn to represent the prime factors of 162. As 162 is not a prime number, it must have multiple factors other than 1 and 162.

All composite numbers have more than two factors, creating a multi-tiered factor tree. For prime numbers, this factor tree is only restricted to one level. But for composite numbers, the factor tree starts from double tiered onwards.

The factor tree of 162 can be seen clearly in figure 2 attached in this section below:

Figure 2

Factors of 162 in Pairs

Factors of 162 in pairs are also called factor pairs in more mathematical terms. These are a pair of numbers from among the factors of 162, which always give the original number 162 after their multiplication.

This property makes them quite distinct from other arrangements of factors because not all arrangements in a couplet will give 162 when multiplied by each other. 

Now factors are not only positive in nature for negative numbers, but we also have negative factors. So the existence of negative factors implies that there must be an existence of negative factor pairs as well. 

This section will look at both the positive and negative factor pairs. But let us first write down the factors of 162:

Factors of 162 =  1, 2, 3, 6, 9, 18, 27, 54, 81, and 162

If we take any random two factors from this list, they will not make a factor pair. Only the factor pairs mentioned below are the true factor pairs of 162:

Factor pairs of 162 = (1, 162), (2, 81), (3, 54), (6, 27), (9, 18)

As 162 has ten factors, it is obvious that it will have 5-factor pairs. These factor pairs are also the positive factor pairs, but in order to find out the negative factor pairs, we add a negative (-) symbol before all numbers to make them negative:

Negative factor pairs of 162 = (-1, -162), (-2, -81), (-3, -54), (-6, -27), (-9, -18)

Factors of 162 Solved Examples

In this section, we have solved some examples that can help you to solidify your learning of the process of factorization:

Example 1

Find out the common factors between 162, 163, and 164.

Solution

First, we will find out the factors of 162, 163, and 164 in order to find out their common factors:

Factors of 162 =  1, 2, 3, 6, 9, 18, 27, 54, 81, and 162

The factors of 163 are:

Factors of 163 = 1, and 163.

Similarly, the factors of 164 are:

Factors of 164 = 1, 2, 4, 41, 82, and 164

Now that we have all the factors of all the numbers, we will try to find out the common factors which exist among these numbers. 

After looking at their factor list, the common factors for 162, 163, and 164 turn out to be only one. This factor is one because it is the only common factor among all of them.

Therefore, the common factor between 162, 163, and 164 is 1.

Example 2

Find out the prime factors of 162 and calculate their average.

Solution

This question does not specify the method to find the prime factors of 162. Still, we are aware of the significant difference between prime factorization and the division method, so we know which method to choose if we want to find out the prime factors of any number.

The method we choose is prime factorization, which is as follows:

First, find out the prime factors of 162:

162 $\div$ 2 = 81

81 $\div$ 3 = 27

27 $\div$ 3 = 9

9 $\div$ 3 = 3

3 $\div$ 3 = 1

The prime factors of 162 are: 2, 3, 3, 3, 3.

The average of their factors can be calculated by:

Average = Sum of all factors of 162/ Total number of factors

Average =( 2 + 3 + 3 + 3 + 3) / 5

Average = 14 / 5

Average  = 2.8

Therefore, the average of the factors of 162 is 2.8.

Example 3

Write down the factors of 162 and calculate the sum of its factors along with their product.

Solution

Using the division method, the factors of 162 turn out to be as follows:

Factors of 162 = 1, 2, 3, 6, 9, 18, 27, 54, 81, and 162

For the next part of the question, we will now calculate the sum of these factors; the sum of these factors is:

Sum of factors of 162 = 1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 + 162

Sum of factors of 162 = 363

Therefore, the sum of factors of 162 is equal to a total of 363.

We also have to calculate the product of the factors of 162:

Product of factors of 162 = 1 x 2 x 3 x 6 x 9 x 18 x 27 x 54 x 81 x 162

Product of factors of 162 = 1.11^11

Hence, the sum of factors of 162 is 363, and their product is equal to 1.11^11.

All images/mathematical drawings are created with GeoGebra. 

Factors of 161 | Factors List | Factors of 163

5/5 - (6 votes)