Factors of 279: Prime Factorization, Methods, and Examples

The factors of 279 are the integers that divide 279 evenly without any remainder. The number 279 is an odd composite with six factors in total. A number can have a positive and negative number.

Factors Of 279

 A negative factor is the same as a positive factor with a negative sign.   

Factors of 279

Here are the factors of number 279.

Factors of 279: 1, 3, 9, 31, 93, 279 

Negative Factors of 279

The negative factors of 279 are similar to their positive aspects, just with a negative sign.

Negative Factors of 279: –1, -3, -9, -31, -93, -279 

Prime Factorization of 279

The prime factorization of 279 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 3 x 31

In this article, we will learn about the factors of 279 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 279?

The factors of 279 are 1, 3, 9, 31, 93, and 279. These numbers are the factors as they do not leave any remainder when divided by 279.

The factors of 279 are classified as prime numbers and composite numbers. The prime factors of the number 279 can be determined using the prime factorization technique.

How To Find the Factors of 279?

You can find the factors of 279 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 279, create a list containing the numbers that are exactly divisible by 279 with zero remainders. One important thing to note is that 1 and 279 are the 279’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 279 are determined as follows:

\[\dfrac{279}{1} = 279\]

\[\dfrac{279}{3} = 93\]

\[\dfrac{279}{9} = 31\]

\[\dfrac{279}{279} = 1\]

Therefore, 1, 3, 9, 31, 93, and 279 are the factors of 279.

Total Number of Factors of 279

For 279, there are six positive factors and six negative ones. So in total, there are twelve factors of 279. 

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 X is given as:

Factorization of 279 is 1 x 3$^2$ x 31.

The exponent of 1 and 31 is 1, and 3 is 2.

Adding 1 to each and multiplying them together results in 12.

Therefore, the total number of factors of 279 is twelve. Six are positive, and six 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 279 by Prime FactorizationFactor of 279 by Prime Factorization

The number 279 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 279 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 279, 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 279 can be expressed as:

279 = 3 x 3 x 31

Factors of 279 in PairsFactor of 279 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 279, the factor pairs can be found as:

1 x 279 = 279

3 x 93 = 279 

9 x 31 = 279 

The possible factor pairs of 279 are given as (1, 279), (3, 93), and (9, 31).

All these numbers in pairs, when multiplied, give 279 as the product.

The negative factor pairs of 279 are given as:

-1 x -279 = 279

-3 x -93 = 279 

-9 x -31 = 279 

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, -9, -31, -93, and -279 are called negative factors of 279.

The list of all the factors of 279, including positive as well as negative numbers, is given below.

Factor list of 279: 1, -1, 3, -3, 9, -9, 31, -31, 93, -93, 279, and -279

Factors of 279 Solved Examples

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

Example 1

How many factors of 279 are there?

Solution

The total number of Factors of 279 is six.

Factors of 279 are 1, 3, 9, 31, 93, and 279.

Example 2

Find the factors of 279 using prime factorization.

Solution

The prime factorization of 279 is given as:

279 $\div$ 3 = 93

93 $\div$ 3 = 31  

31 $\div$ 31 = 1 

So the prime factorization of 279 can be written as:

3 x 3 x 31 = 279

Factors of 278|Factors List| Factors of 280