Factors of 488: Prime Factorization, Methods, and Examples

The 488 factors are those numbers that divide the given number 488 exactly. The number’s factor is its component. 

For example, the factors of the number488 can be positive or negative if the supplied number was produced by multiplying two-factor integers.

Factors of 488

Here are the factors of number 488.

Factors of 488: 1, 2, 4, 8, 61, 122, 244 and 488

Negative Factors of 488

The negative factors of 488 are similar to their positive aspects, just with a negative sign.

Negative Factors of 488: -1, -2, -4, -8, -61, -122, -244 and -488

Prime Factorization of 488

The prime factorization of 488 is the way of expressing its prime factors in the product form.

Prime Factorization:  2³ x 61¹

In this article, we will learn about the factors of 488 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 488?

The factors of 488 are 1, 2, 4, 8, 61, 122, 244  and 488. These numbers are the factors as they do not leave any remainder when divided by 488.

The factors of 488 are classified as prime numbers and composite numbers. The prime factors of the number 488 can be determined using the prime factorization technique.

How To Find the Factors of 488?

You can find the factors of 488 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 488, create a list containing the numbers that are exactly divisible by 488 with zero remainders. One important thing to note is that 1 and 488 are the 488’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 488 are determined as follows:

\[\dfrac{488}{1} = 488\]

\[\dfrac{488}{2} = 244\]

\[\dfrac{488}{4} = 122\]

\[\dfrac{488}{8} =   61\]

\[\dfrac{488}{61} =   8\]

\[\dfrac{488}{122} = 4\]

\[\dfrac{488}{244} = 2\]

\[\dfrac{488}{488} = 1\]

Therefore, 1, 2, 4, 8, 61, 122, 244 and 488 are the factors of 488.

Total Number of Factors of 488

For 488, there are 8 positive factors and 8 negative ones. So in total, there are 16 factors of 488. 

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 488 is given as:

Factorization of 488 is 1 x 2³ x 61¹.

The exponent of 1 is 1, 2 is 3, and 61 is 1.

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

Therefore, the total number of factors of 488 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 488 by Prime Factorization

The number 488 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 488 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 488, 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 488 can be expressed as:

488 = 2³ x 61¹

Factors of 488 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 488, the factor pairs can be found as:

1 x 488 = 488

2 x 244  = 488

4 x 122 = 488

8 x 61 = 488

The possible factor pairs of 488 are given as (1, 488),(2, 244), (4, 122), and (8, 61).

All these numbers in pairs, when multiplied, give 488 as the product.

The negative factor pairs of 488 are given as:

-1 x -488 = 488

-2 x -244  = 488

-4 x -122 = 488

-8 x -61 = 488

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, -2, -4, -8, -61, -122, -244 and -488 are called negative factors of 488.

The list of all the factors of 488, including positive as well as negative numbers, is given below.

Factor list of 488: 1,-1, 2,-2,4, -4, 8,-8, 61,-61, 122,-122, 244,-244, 488, and -488

Factors of 488 Solved Examples

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

Example 1

How many factors of 488 are there?

Solution

The total number of Factors of 488 is 16.

Factors of 488 are 1, 2, 4, 8, 61, 122, 244 and 488.

Example 2

Find the factors of 488 using prime factorization.

Solution

The prime factorization of 488 is given as:

488 $\div$ 2 = 244 

244 $\div$ 2 = 122

41 $\div$ 2 = 61

61 $\div$ 61 = 1 

So the prime factorization of 488 can be written as:

2³ x 61¹ = 488

Factors of 487|Factors List| Factors of 489