Factors Of 309Factors of 309: Prime Factorization, Methods, and Examples

The factors of 309 are 1, 3, 103, and 309. The factors are the numbers that are completely divisible by the given number. 

The number 309 is an odd composite with four factors. Let us explore more about the factors of 309 and how to find them.

Factors of 309

Here are the factors of number 309.

Factors of 309: 1, 3, 103, and 309

Negative Factors of 309

The negative factors of 309 are similar to its positive aspects, just with a negative sign.

Negative Factors of 309: –1, -3, -103, and -309

Prime Factorization of 309

The prime factorization of 309 is the way of expressing its prime factors in the product form.

Prime Factorization: 3 x 103

In this article, we will learn about the factors of 309 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 309?

The factors of 309 are 1, 3, 103, and 309. These numbers are the factors as they do not leave any remainder when divided by 309.

The factors of 309 are classified as prime numbers and composite numbers. The prime factors of the number 309 can be determined using the prime factorization technique.

How To Find the Factors of 309?

You can find the factors of 309 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 309, create a list containing the numbers that are exactly divisible by 309 with zero remainders. One important thing to note is that 1 and 309 are 309’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 309 are determined as follows:

\[\dfrac{309}{1} = 309\]

\[\dfrac{309}{3} = 103\]

\[\dfrac{309}{103} = 3\]

\[\dfrac{309}{309} = 1\]

Therefore, 1, 3, 103, and 309 are the factors of 309.

Total Number of Factors of 309

For 309, there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 309. 

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 309 is given as:

Factorization of 309 is 1 x 3 x 103.

The exponent of 1, 3, and 103 is 1.

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

Therefore, the total number of factors of 309 is 8. 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 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 309 by Prime Factorization

The number 309 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.prime factorization of 309

Before finding the factors of 309 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 309, 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 309 can be expressed as:

309 = 3 x 103

Factors of 309 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.Factors of 309 in Pairs

For 309, the factor pairs can be found as:

1 x 309 = 309

3 x 103 = 309 

The possible factor pairs of 309 are given as (1, 309) and (3, 103).

All these numbers in pairs, when multiplied, give 309 as the product.

The negative factor pairs of 309 are given as:

1 x -309 = 309

-3 x -103 = 309 

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, -103, and -309 are called negative factors of 309.

Factors of 309 Solved Examples

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

Example 1

How many factors of 309 are there?

Solution

The total number of Factors of 309 is four.

Factors of 309 are 1, 3, 103, and 309.

Example 2

Find the factors of 309 using prime factorization.

Solution

The prime factorization of 309 is given as:

309 $\div$ 3 = 103 

103 $\div$ 103 = 1 

So the prime factorization of 103 can be written as:

3 x 103 = 309

Factors of 308|Factors List| Factors of 310