# Factors of 357: Prime Factorization, Methods, and Examples

There are eight factors of 357. The factors are those numbers that give a zero remainder when divided by the actual number.

357 is an odd composite number; further details about the factors of 357 are given in the article.

### Factors of 357

Here are the factors of number 357.

Factors of 357: 1, 3, 7, 17, 21, 51, 119, 357.

### Negative Factors of 357

The negative factors of 357 are similar to their positive aspects, just with a negative sign.

Negative Factors of 357: -1, -3, -7, -17, -21, -51, -119, -357

### Prime Factorization of 357

The prime factorization of 357 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 7 x 17

In this article, we will learn about the factors of 357 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

## What Are the Factors of 357?

The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357. These numbers are the factors as they do not leave any remainder when divided by 357.

The factors of 357 are classified as prime numbers and composite numbers. The prime factors of the number 357 can be determined using the prime factorization technique.

## How To Find the Factors of 357?

You can find the factors of 357 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 357, create a list containing the numbers that are exactly divisible by 357 with zero remainders. One important thing to note is that 1 and 357 are the 357’s factors as every natural number has one and the number itself as its factor.

One is also called the universal factor of every number. The factors of 357 are determined as follows:

$\dfrac{357}{1} = 357$

$\dfrac{357}{3} = 119$

$\dfrac{357}{7} = 51$

$\dfrac{357}{17} = 21$

$\dfrac{357}{357} = 1$

Therefore, 1, 3, 7, 17, 21, 51, 119, and 357 are the factors of 357.

### Total Number of Factors of 357

For 357, there are eight positive factors and eight negative ones. So in total, there are 16 factors of 357.

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 357 is given as:

Factorization of 357 is 1, 3, 7, 17, 21, 51, 119, and 357.

The exponent of 1, 3, 7, 17, 21, 51, 119, and 357 is 1.

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

Therefore, the total number of factors of 357 is 16. 8 are positive, and eight 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 357 by Prime Factorization

The number 357 is 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 357 using prime factorization, let us determine 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 357, 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 357 can be expressed as:

357 = 3 x 7 x 17

## Factors of 357 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 357, the factor pairs can be found as:

1 x 357 = 357

3 x 119 = 357

7 x 51 = 357

17 x 21 = 357

The possible factor pairs of 357 are given as (1, 357), (3, 119), (7, 51), and (17, 21).

All these numbers in pairs, when multiplied, give 357 as the product.

The negative factor pairs of 357 are given as:

-1 x -357 = -357

-3 x -119 = -357

-7 x -51 = -357

-17 x -21 = -357

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, -3, -7, -17, -21, -51, -119, -357 are called negative factors of 357.

The list of all the factors of 357, including positive and negative numbers, is given below.

Factor list of 357: 1, -1, 3, -3, 7, -7, 17, -17, 21, -21, 51, -51, 119, -119, 357 and -357

## Factors of 357 Solved Examples

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

### Example 1

How many factors of 357 are there?

### Solution

The total number of Factors of 357 is 16.

Factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357.

### Example 2

Find the factors of 357 using prime factorization.

### Solution

The prime factorization of 357 is given as:

357 $\div$ 17 = 21

21 $\div$ 21 = 1

So the prime factorization of 357 can be written as:

21 x 17 = 357