 # Factors of 364: Prime Factorization, Methods, and Examples

The numbers that entirely divide 364 among them are known as the factors of 364. These integers result in a whole number quotient and a remainder of zero.

### Factors of 364

Here are the factors of number 364.

Factors of 364:1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 ,364

### Negative Factors of 364

The negative factors of 364 are similar to their positive aspects, just with a negative sign.

Negative Factors of 364: -1, -2, -4, -7, -13, -14, -26, -28, -52, -91 , -184,  -364

### Prime Factorization of 364

The prime factorization of 364 is the way of expressing its prime factors in the product form.

Prime Factorization:  2 x 2 x 7 x 13

In this article, we will learn about the factors of 364 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 364?

The factors of 364 are 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 and 364. These numbers are the factors as they do not leave any remainder when divided by 364.

The factors of 364 are classified as prime numbers and composite numbers. The prime factors of the number 364 can be determined using the prime factorization technique.

## How To Find the Factors of 364?

You can find the factors of 364 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 364, create a list containing the numbers that are exactly divisible by 364 with zero remainders. One important thing to note is that 1 and 364 are the 364’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 364 are determined as follows:

$\dfrac{364}{1} = 364$

$\dfrac{364}{2} = 182$

$\dfrac{364}{4} = 91$

$\dfrac{364}{7} = 52$

$\dfrac{364}{364} = 1$

Therefore, 1, 2, 4, 7, and 364 are the factors of 364.

### Total Number of Factors of 364

For 364, there are 12 positive factors and 12 negative ones. So in total, there are 24 factors of 364.

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 364 is given as:

Factorization of 364 is 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 ,364.

The exponent of 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 and 364 is 1.

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 364 is 24. 12 is positive, and 12 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 364 by Prime Factorization

The number 364 is a composite/prime number. Prime factorization is a valuable technique for finding the number’s prime factors and expressing the number as the product of its prime factors. Before finding the factors of 364 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 364, start dividing by its most minor 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 364 can be expressed as:

364 = 2 x 182

## Factors of 364 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 given. For 364, the factor pairs can be found as:

1 x 364 = 364

2 x 182 = 364

4 x 91 = 364

7 x 52 = 364

13 x 28 = 364

14 x 26 = 364

The possible factor pairs of 364 are given as (1, 364), (2, 182 ),(4, 91),(7, 52), (13, 28) and (14, 26).

All these numbers in pairs, when multiplied, give 364 as the product.

The negative factor pairs of 364 are given as:

-1 x -364 = 364

-2 x -182 = 364

-4 x -91 = 364

-7 x -52 = 364

-13 x -28 = 364

-14 x -26 = 364

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, -7, -13, -14, -26, -28, -52, -91 , -184,  -364 are called negative factors of 364.

The list of all the factors of 364, including positive as well as negative numbers, is given below.

Factor list of 364:1,-1 ,2, -2, 4, -4, 7, -7, 13, -13, 14, -14, 26, -26, 28, -28, 52, -52, 91, -91, 182 , -182, 364, and -364

## Factors of 364 Solved Examples

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

### Example 1

How many factors of 364 are there?

### Solution

The total number of Factors of 364 is 24.

Factors of 364 are1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182 ,364.

### Example 2

Find the factors of 364 using prime factorization.

### Solution

The prime factorization of 364 is given as:

364 $\div$ 2 = 182

182 $\div$ 2 = 91

91 $\div$ 7 = 13

13 $\div$ 13 = 1

So the prime factorization of 364 can be written as:

2 x 2 x 7 x 13 = 364