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Factors of 339: Prime Factorization, Methods, and Examples

The factors of 339 are numbers that can be divided by 339. There are four factors of number 339. The factors of 339 are positive and negative integers. 

In this lesson, we will discuss more the factors of number 339.

Factors of 339

Here are the factors of number 339.

Factors of 339: 1, 3, 113, 339

Negative Factors of 339

The negative factors of 339 are similar to their positive aspects, just with a negative sign.

Negative Factors of 339: –1, -3, -113, -339

Prime Factorization of 339

The prime factorization of 339 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 339

In this article, we will learn about the factors of 339 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 339?

The factors of 339 are 1, 3, 113, and 339. These numbers are the factors as they do not leave any remainder when divided by 339.

The factors of 339 are classified as prime numbers and composite numbers. The prime factors of the number 339 can be determined using the prime factorization technique.

How To Find the Factors of 339?

You can find the factors of 339 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 339, create a list containing the numbers divisible by 339 with zero remainders. One important thing to note is that 1 and 339 are the 339’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 339 are determined as follows:

\[\dfrac{339}{1} = 339\]

\[\dfrac{339}{3} = 113\]

Therefore, 1, 3, 113, and 339 are the factors of 339.

Total Number of Factors of 339

For 39, there are four positive factors and four negative ones. So in total, there are eight factors of 339. 

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 339 is given as:

Factorization of 339 is 1 x 3 x 113.

The exponent of 1, 3, and 113 is 1.

Adding 1 to each and multiplying them together results in 8.

Therefore, the total number of factors of 339 is eight. Four are positive, and four 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 2 as its prime factor, the smallest prime factor.

Factors of 339 by Prime Factorization

The number 339 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 339 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 339, 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 339 can be expressed as:

339 = 3 x 113

Factors of 339 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 339, the factor pairs can be found as:

1 x 339 = 339

3 x 113 = 339

The possible factor pairs of 339 are given as (1, 339) and (3, 113 ).

All these numbers in pairs, when multiplied, give 339 as the product.

The negative factor pairs of 339 are given as:

-1 x -339 = 339 

-3 x -113 = 339

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, -113, and -339 are called negative factors of 339.

The list of all the factors of 339, including positive and negative numbers, is given below.

Factor list of 339: 1, 3, 113, 339, –1, -3, -113, and -339

Factors of 339 Solved Examples

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

Example 1

How many factors of 339 are there?

Solution

The total number of Factors of 339 is 4.

Factors of 339 are 1, 3, 113, and 339.

Example 2

Find the factors of 339 using prime factorization.

Solution

The prime factorization of 339 is given as:

339 $\div$ 3 = 113 

113 $\div$ 113 = 1 

So the prime factorization of 339 can be written as:

3 x 113 = 339

Factors of 338|Factors List| Factors of 340

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