 # Factors of 164: Prime Factorization, Methods, and E164amples

The factors of 164 can be grouped as the set of natural numbers that are wholly divisible by the number 164. 164 is an even number as well as a composite. The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers. ### Factors of 164

Here are the factors of number 164.

Factors of 164: 1, 2, 4, 41, 82, 164

### Negative Factors of 164

The negative factors of 164 are similar to its positive factors, just with a negative sign.

Negative Factors of 164: -1, -2, -4, -41, -82, and -164

### Prime Factorization of 164

The prime factorization of 164 is the way of expressing its prime factors in the product form. Prime Factorization: 2 x 2 x 41

In this article, we will learn about the factors of 164 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 164?

The factors of 164 are 1, 2, 4, 41, 82, and 164. All of these numbers are the factors as they do not leave any remainder when divided by 164.

The factors of 164 are classified as prime numbers and composite numbers. The prime factors of the number 164 can be determined using the technique of prime factorization.

## How To Find the Factors of 164?

You can find the factors of 164 by using the rules of divisibility. The divisibility rule states that any number, when divided by any other natural number, is said to be divisible by the number if the quotient is the whole number and the resulting remainder is zero.

To find the factors of 164, create a list containing the numbers exactly divisible by 164 with zero remainders. One important thing to note is that 1 and 164 are the 164’s factors as every natural number has 1 and the number itself as its factor.

1 is also called the universal factor of every number. The factors of 164 are determined as follows:

$\dfrac{164}{1} = 164$

$\dfrac{164}{2} = 82$

$\dfrac{164}{4} = 41$

$\dfrac{164}{164} = 1$

The quotients, as well as the divisors, are the factors of number 164. Therefore, 1, 2, 4, 41, 82, and 164 are the factors of 164.

### Total Number of Factors of 164

For 164 there are n positive factors and n negative ones. So in total, there are m factors of 164.

To find the total number of factors of the given number, follow the procedure mentioned below:

1. Find the factorization/prime factorization of the given number.
2. Demonstrate the prime factorization of the number in the form of exponent form.
3. Add 1 to each of the exponents of the prime factor.
4. Now, multiply the resulting exponents together. This obtained product is equivalent to the total number of factors of the given number.

By following this procedure the total number of factors of 164 is given as:

The factorization of 164 is 1 x 2$^2$ x 41.

The exponent of 1 and 41 is 1. The exponent of 2 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 164 is 12. 6 are positive and 6 factors are negative.

### Important Notes

Here are some essential points that must be considered while finding the factors of any given number:

• The factor of any given number must be a whole number.
• The factors of the number cannot be in the form of decimals or fractions.
• Factors can be positive as well as negative.
• Negative factors are the additive inverse of the positive factors of a given number.
• The factor of a number cannot be greater than that number.
• Every even number has 2 as its prime factor, the smallest prime factor.

## Factors of 164 by Prime Factorization

The number 164 is a composite. Prime factorization is a useful technique for finding the number’s prime factors and e164pressing the number as the product of its prime factors.

Before finding the factors of 164 using prime factorization, let us find out what prime factors are. Prime factors are the factors of any given number that are only divisible by 1 and themselves.

To start the prime factorization of 164, start dividing by its smallest prime factor. First, determine that the given number is either even or odd. If it is an even number, then 2 will be the smallest prime factor.

Continue splitting the quotient obtained until 1 is received as the quotient. The prime factorization of 164 can be expressed as:

164 = 2$^2$  x 41

## Factors of 164 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Factor pairs can be more than one depending on the total number of factors of the given numbers. For 164, the factor pairs can be found as:

1 x 164 = 164

2 x 82 = 164

4 x 41 = 164

The possible factor pairs of 164 are given as (1, 164), (2, 82), and (4, 41 ).

All these numbers in pairs, when multiplied, give 164 as the product.

The negative factor pairs of 164 are given as:

-1 x -164 = 164

-2 x -82 = 164

-4 x -41 = 164

It is important to note that in negative factor pairs, the minus sign has been multiplied by the minus sign due to which the resulting product is the original positive number. Therefore, -1, -2, -4, -41, -82, and -164 are called negative factors of 164.

The list of all the factors of 164 including positive and negative numbers is given below.

Factor list of 164: 1, -1, 2, -2, 4, -4, 41, -41, 82, -82, 164, -164.

## Factors of 164 Solved Examples

To better understand the concept of factors, let’s solve some examples.

### Example 1

How many factors of 164 are there?

### Solution

The total number of Factors of 164 is 6.

Factors of 164 are 1, 2, 4, 41, 82, and 164.

### Example 2

Find the factors of 164 using prime factorization.

### Solution

The prime factorization of 164 is given as:

164 $\div$ 2 = 82

82 $\div$ 2 = 41

41 $\div$ 41 = 1

So the prime factorization of 164 can be written as:

2 x 2 x 41 = 164