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Factors of 399: Prime Factorization, Methods, and Examples

The factors of 399 are the numbers that give 399 as the product when they are multiplied together. Such numbers also form factor pairs. 

The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.

Factors of 399

Here are the factors of number 399.

Factors of 399: 1, 3, 7, 19, 21, 57, 133, 399

Negative Factors of 399

The negative factors of 399 are similar to its positive aspects, just with a negative sign.

Negative Factors of 399: -1, -3, -7, -19, -21, -57, -133, and -399

Prime Factorization of 399

The prime factorization of 399 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 7 x 19

In this article, we will learn about the factors of 399 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 399?

The factors of 399 are 1, 3, 7, 19, 21, 57, 133, and 399. These numbers are the factors as they do not leave any remainder when divided by 399.

The factors of 399 are classified as prime numbers and composite numbers. The prime factors of the number 399 can be determined using the prime factorization technique.

How To Find the Factors of 399?

You can find the factors of 399 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 399, create a list containing the numbers that are exactly divisible by 399 with zero remainders. One important thing to note is that 1 and 399 are the 399’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 399 are determined as follows:

\[\dfrac{399}{1} = 399\]

\[\dfrac{399}{3} = 133\]

\[\dfrac{399}{7} = 57\]

\[\dfrac{399}{19} = 21\]

Therefore, 1, 3, 7, and 19 along with their quotients 21, 57, 133, and 399 are the factors of 399.

Total Number of Factors of 399

For 399, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 399. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the 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 399 is given as:

Factorization of 399 is 3 x 7 x 19.

The exponent of all factors is 1.

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

Therefore, the total number of factors of 399 is 16. 8 are positive, and 8 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 399 by Prime Factorization

The number 399 is a composite 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 399 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 399, 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 399 can be expressed as:

399 = 3 x 7 x 19

Factors of 399 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 399, the factor pairs can be found as:

1 x 399 = 399

3 x 133 = 399

7 x 57 = 399

19 x 21 = 399 

The possible factor pairs of 399 are given as (1, 399), (3, 133), (7, 57), and (19, 21).

All these numbers in pairs, when multiplied, give 399 as the product.

The negative factor pairs of 399 are given as:

-1 x -399 = 399

-3 x -133 = 399

-7 x -57 = 399

-19 x -21 = 399 

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, -19, -21, -57, -133, and -399 are called negative factors of 399.

The list of all the factors of 399, including positive as well as negative numbers, is given below.

Factor list of 399: 1, -1, 3, -3, 7, -7, 19, -19, 57, -57, 21, -21, 133, -133, 399, and -399

Factors of 399 Solved Examples

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

Example 1

How many factors of 399 are there?

Solution

The total number of Factors of 399 is 8.

Factors of 399 are 1, 3, 7, 19, 21, 57, 133, and 399.

Example 2

Find the factors of 399 using prime factorization.

Solution

The prime factorization of 399 is given as:

399 $\div$ 3 = 133 

133 $\div$ 7 = 19

19 $\div$ 19 = 1 

So the prime factorization of 399 can be written as:

3 x 7 x 19 = 399

Factors of 398|Factors List| Factors of 400

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