# Factors of 374: Prime Factorization, Methods, and Examples

The factors of 374 are the listing of the numbers that divide 374 evenly without any remainder. The factors of 374 can be positive as well as negative.

In this article, we will find out how to use division method and prime factorization technique to determine the factors of 374.

### Factors of 374

Here are the factors of number 374.

Factors of 374: 1, 2, 11, 17, 22, 34, 187, and 374

### Negative Factors of 374

The negative factors of 374 are similar to its positive aspects, just with a negative sign.

Negative Factors of 374: –1, -2, -11, -17, -22, -34, -187, and -374

### Prime Factorization of 374

The prime factorization of 374 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 11 x 17

In this article, we will learn about the factors of 374 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 374?

The factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374. These numbers are the factors as they do not leave any remainder when divided by 374.

The factors of 374 are classified as prime numbers and composite numbers. The prime factors of the number 374 can be determined using the prime factorization technique.

## How To Find the Factors of 374?

You can find the factors of 374 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 374, create a list containing the numbers that are exactly divisible by 374 with zero remainders. One important thing to note is that 1 and 374 are the 374’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 374 are determined as follows:

$\dfrac{374}{1} = 374$

$\dfrac{374}{2} = 187$

$\dfrac{374}{11} = 34$

$\dfrac{374}{17} = 22$

Therefore, 1, 2, 11, 17, 22, 34, 187, and 374 are the factors of 374.

### Total Number of Factors of 374

For 374, there are eight positive factors and eight negative ones. So in total, there are sixteen factors of 374.

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 374 is given as:

Factorization of 374 is 1 x 2 x 11 x 17.

The exponent of 1, 2, 11, and 17 is 1.

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

Therefore, the total number of factors of 374 is 16. 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 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 374 by Prime Factorization

The number 374 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 374 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 374, 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 374 can be expressed as:

374 = 2 x 11 x 17

## Factors of 374 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 374, the factor pairs can be found as:

1 x 374 = 374

2 x 187 = 374

11 x 34 = 374

17 x 22 = 374

The possible factor pairs of 374 are given as (1, 374), (2,187), (11,34), and (17,22).

All these numbers in pairs, when multiplied, give 374 as the product.

The negative factor pairs of 374 are given as:

-1 x -374 = 374

-2 x -187 = 374

-11 x -34 = 374

-17 x -22 = 374

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, -11, -17, -22, -34, -187, and -374 are called negative factors of 374.

The list of all the factors of 374, including positive as well as negative numbers, is given below.

Factor list of 374: 1, -1, 2, -2, 11, -11, 17, -17, 22, -22, 34, -34, 187, -187, 374, and -374

## Factors of 374 Solved Examples

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

### Example 1

How many factors of 374 are there?

### Solution

The total number of Factors of 374 is 8.

Factors of 374 are 1, 2, 11, 17, 22, 34, 187, and 374.

### Example 2

Find the factors of 374 using prime factorization.

### Solution

The prime factorization of 374 is given as:

374 $\div$ 2 = 187

187 $\div$ 11 = 17

17 $\div$ 17 = 1

So the prime factorization of 374 can be written as:

2 x 11 x 17 = 374