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Factors of 489: Prime Factorization, Methods, and Examples

One of the components is the whole number that entirely divides 489. The odd and composite numbers are 489. It implies that there are more than two independent contributing factors. 

The result can be obtained by multiplying any two integer factors, regardless of the components’ signs.

Factors of 489

Here are the factors of number 489.

Factors of 489: 1, 3, 163 and 489

Negative Factors of 489

The negative factors of 489 are similar to their positive aspects, just with a negative sign.

Negative Factors of 489: -1, -3, -163 and -489

Prime Factorization of 489

The prime factorization of 489 is the way of expressing its prime factors in the product form.

Prime Factorization: 31 x 1631

In this article, we will learn about the factors of 489 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 489?

The factors of 489 are 1, 3, 163, and 489. These numbers are the factors as they do not leave any remainder when divided by 489.

The factors of 489 are classified as prime numbers and composite numbers. The prime factors of the number 489 can be determined using the prime factorization technique.

How To Find the Factors of 489?

You can find the factors of 489 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 489, create a list containing the numbers that are exactly divisible by 489 with zero remainders. One important thing to note is that 1 and 489 are the 489’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 489are determined as follows:

\[\dfrac{489}{1} = 489\]

\[\dfrac{489}{3} = 163\]

\[\dfrac{489}{163} = 3\]

\[\dfrac{489}{489} = 1\]

Therefore, 1, 3, 163, and 489 are the factors of 489.

Total Number of Factors of 489

For 489, there are  4 positive factors and 4 negative ones. So in total, there are 8 factors of 489. 

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 489 is given as:

Factorization of 489 is  31 x 1631.

The exponent of 3 and 163 is 1.

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

Therefore, the total number of factors of 489 is 8. 4 is positive, and 4 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 489 by Prime Factorization

The number 489 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 489 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 489, 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 489 can be expressed as:

489 = 31 x 1631

Factors of 489 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 489, the factor pairs can be found as:

1 x 489 = 489

3 x 163 = 489

The possible factor pairs of 489 are given as (1, 489) and (3, 163 ).

All these numbers in pairs, when multiplied, give 489 as the product.

The negative factor pairs of 489 are given as:

-1 x -489 = 489

-3 x -163 = 489

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, -163, and -489 are called negative factors of 489.

The list of all the factors of 489, including positive as well as negative numbers, is given below.

Factor list of 489: 1,-1, 3,-3, 163,-163, 489, and -489

Factors of 489 Solved Examples

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

Example 1

How many factors of 489 are there?

Solution

The total number of Factors of 489 is 8.

Factors of 489 are 1, 3, 163, and 489.

Example 2

Find the factors of 489 using prime factorization.

Solution

The prime factorization of 489 is given as:

489 $\div$ 3 = 163 

163 $\div$ 163= 1 

So the prime factorization of 489 can be written as:

31 x 1631 = 489

Factors of 488|Factors List| Factors of 490

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