banner

Factors of 459: Prime Factorization, Methods, and Examples

The factors of 459 are numbers that, when divided by 459, leave zero as the remainder. This means the numbers that ultimately divide the given number are named as their factors. 

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 459

Here are the factors of number 459.

Factors of 459: 1, 3, 9, 17, 27, 51, 153 and 459

Negative Factors of 459

The negative factors of 459 are similar to its positive aspects, just with a negative sign.

Negative Factors of 459: -1, -3, -9, -17, -27, -51, -153 and -459

Prime Factorization of 459

The prime factorization of 459 is the way of expressing its prime factors in the product form.

Prime Factorization: 33 × 17

In this article, we will learn about the factors of 459 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 459?

The factors of 459 are a, b, c, and 459. These numbers are the factors as they do not leave any remainder when divided by 459.

The factors of 459 are classified as prime numbers and composite numbers. The prime factors of the number 459 can be determined using the prime factorization technique.

How To Find the Factors of 459?

You can find the factors of 459 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 459, create a list containing the numbers that are exactly divisible by 459 with zero remainders. One important thing to note is that 1 and 459 are the 459’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 459 are determined as follows:

\[\dfrac{459}{1} = 459\]

\[\dfrac{459}{3} = 153\]

\[\dfrac{459}{9} = 51\]

\[\dfrac{459}{17} = 27\]

\[\dfrac{459}{27} = 17\]

\[\dfrac{459}{51} = 9\]

\[\dfrac{459}{153} = 3\]

\[\dfrac{459}{459} = 1\]

Therefore, 1, 3, 9, 17, 27, 51, 153, and 459 are the factors of 459.

Total Number of Factors of 459

For 459, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 459. 

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 459 is given as:

Factorization of 459 is 1, 3, 9, 17, 27, 51, 153 and 459.

The exponent of 1, 3, 9, 17, 27, 51, 153, and 459 is 1.

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

Therefore, the total number of factors of 459 is 16. 8 is 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 459 by Prime Factorization

The number 459 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 459 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 459, 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 459 can be expressed as:

459 = 33 × 17

Factors of 459 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 459, the factor pairs can be found as:

1 x 459 = 459

3 x 153 = 459

9 x 51 = 459

17 x 27 = 459

The possible factor pairs of 459 are given as (1, 459), (3, 153), (9, 51), and (17, 27).

All these numbers in pairs, when multiplied, give 459 as the product.

The negative factor pairs of 459 are given as:

-1 x -459 = 459

-a x -b = 459

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, -17, -27, -51, -153 and -459 are called negative factors of 459.

The list of all the factors of 459, including positive as well as negative numbers, is given below.

Factor list of 459: 1,-1, 3,-3, 9,-9, 17,-17, 27,-27,51, -51,153, -153,459 and -459

Factors of 459 Solved Examples

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

Example 1

How many factors of 459 are there?

Solution

The total number of Factors of 459 is 16.

Factors of 459 are 1, 3, 9, 17, 27, 51, 153 and 459.

Example 2

Find the factors of 459 using prime factorization.

Solution

The prime factorization of 459 is given as:

459 $\div$ 3 = 153

153 $\div$ 3 = 51 

51 $\div$ 3 =17

17 $\div$ 17 = 1

So the prime factorization of 459 can be written as:

33 × 17 = 459

Factors of 458|Factors List| Factors of 460

5/5 - (5 votes)