 # Factors of 344: Prime Factorization, Methods, and Examples

The factors of 344 are the list of integers that divide 344 fully without leaving anything behind. In this article, we will discuss the factors of 344, how to find them using various techniques, and solve some examples to understand better.

### Factors of 344

Here are the factors of number 344.

Factors of 344: 1, 2, 4, 8, 43, 86, 172, and 344

### Negative Factors of 344

The negative factors of 344 are similar to their positive aspects, just with a negative sign.

Negative Factors of 344: –1, -2, -4, -8, -43, -86, -172, and -344

### Prime Factorization of 344

The prime factorization of 344 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 2 x 43

In this article, we will learn about the factors of 344 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 344?

The factors of 344 are 1, 2, 4, 8, 43, 86, 172, and 344. These numbers are the factors as they do not leave any remainder when divided by 344.

The factors of 344 are classified as prime numbers and composite numbers. The prime factors of the number 344 can be determined using the prime factorization technique.

## How To Find the Factors of 344?

You can find the factors of 344 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 344, create a list containing the numbers exactly divisible by 344 with zero remainders. One important thing to note is that 1 and 344 are the 344’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 344 are determined as follows:

$\dfrac{344}{1} = 344$

$\dfrac{344}{2} = 172$

$\dfrac{344}{4} = 86$

$\dfrac{344}{8} = 43$

Therefore, 1, 2, 4, 8, 43, 86, 172, and 344 are the factors of 344.

### Total Number of Factors of 344

For 344, there are eight positive factors and eight negative ones. So in total, there are sixteen factors of 344.

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 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 344 is given as:

Factorization of 344 is 1 x 2$^3$ x 43.

The exponent of 1 and 43 is 1. The exponent of 2 is 3.

Adding 1 to each and multiplying them together results in 16.

Therefore, the total number of factors 344 is sixteen. Eight are positive, and eight 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 number factors 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 two as its prime factor, the smallest prime factor.

## Factors of 344 by Prime Factorization

The number 344 is a composite. 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 X 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 one and themselves.

To start the prime factorization of 344, divide 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 344 can be expressed as:

344 = 2 x 2 x 2 x 43

## Factors of 344 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. For 344, the factor pairs can be found as:

1 x 344 = 344

2 x 172 = 344

4 x 86 = 344

8 x 43 = 344

The possible factor pairs of 344 are given as (1, 344), (2, 172), (4, 86), and (8, 43).

All these numbers in pairs, when multiplied, give 344 as the product.

The negative factor pairs of 344 are given as:

1 x -344 = 344

-2 x -172 = 344

-4 x -86 = 344

-8 x -43 = 344

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, -8, -43, -86, -172, and -344 are called negative factors of 344.

## Factors of 344 Solved Examples

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

### Example 1

How many factors of 344 are there?

### Solution

The total number of Factors of 344 is eight.

Factors of 344 are 1, 2, 4, 8, 43, 86, 172 and 344.

### Example 2

Find the factors of 344 using prime factorization.

### Solution

The prime factorization of 344 is given as:

344 $\div$ 2 = 172

172 $\div$ 2 = 86

86 $\div$ 2 = 43

43 $\div$ 43 = 1

So the prime factorization of 344 can be written as:

2 x 2 x 2 x 43 = 344