Factors of 478: Prime Factorization, Methods, and Examples

The factors of 478 are the numbers that can be paired such that when multiplied result in 478. The factors of 478 are positive and negative. 478 is an even number. 

It is also called a composite number as it has four factors in total.

Factors of 478

Here are the factors of number 478.

Factors of 478: 1, 2, 239, and 278

Negative Factors of 478

The negative factors of 478 are similar to their positive aspects, just with a negative sign.

Negative Factors of 478: –1, -2, -239, and -278

Prime Factorization of 278

The prime factorization of 278 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 239

In this article, we will learn about the factors of 478 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 478?

The factors of 478 are 1, 2, 239, and 278. These numbers are the factors as they do not leave any remainder when divided by 478.

The factors of 478 are classified as prime numbers and composite numbers. The prime factors of the number 478 can be determined using the prime factorization technique.

How To Find the Factors of 478?

You can find the factors of 478 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 478, create a list containing the numbers that are exactly divisible by 478 with zero remainders. One important thing to note is that 1 and 478 are 478’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 478 are determined as follows:

\[\dfrac{478}{1} = 478\]

\[\dfrac{478}{2} = 239\]

Therefore, 1, 2, 239, and 278 are the factors of 478.

Total Number of Factors of 478

For 478, there are four positive factors and four negative ones. So in total, there are eight factors of 478. 

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 478 is given as:

Factorization of 478 is 1 x 2 x 239.

The exponent of 1, 2, and 239 is 1.

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

Therefore, the total number of factors of 478 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 478 by Prime Factorization

The number 478 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 478 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 478, 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 478 can be expressed as:

478 = 2 x 239

Factors of 478 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 478, the factor pairs can be found as:

1 x 478 = 478

2 x 239 = 478

The possible factor pairs of 478 are given as (1, 478) and (2, 239).

All these numbers in pairs, when multiplied, give 478 as the product.

The negative factor pairs of 478 are given as:

-1 x -478 = 478

-2 x -239 = 478

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, -239, and -278 are called negative factors of 478.

The list of all the factors of 478, including positive as well as negative numbers, is given below.

Factor list of 478: 1, –1, 2, -2, 239, -239, 278, and -278

Factors of 478 Solved Examples

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

Example 1

How many factors of 478 are there?

Solution

The total number of Factors of 478 is four.

Factors of 478 are 1, 2, 239, and 278.

Example 2

Find the factors of 478 using prime factorization.

Solution

The prime factorization of 478 is given as:

478 $\div$ 2 = 239 

239 $\div$ 239 = 1 

So the prime factorization of 478 can be written as:

2 x 239 = 478

Factors of 477|Factors List| Factors of 479