Factors of 476: Prime Factorization, Methods, and Examples

The factors of 476 are the listings of integers that can divide 476 evenly. The number 476 is a composite number because it has more than two factors. It has twelve factors in total. 

Let us dig in further to find out more about the factors of 476.

Factors of 476

Here are the factors of number 476.

Factors of 476: 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476 

Negative Factors of 476

The negative factors of 476 are similar to their positive aspects, just with a negative sign.

Negative Factors of 476: –1, -2, -4, -7, -14, -17, -28, -34, -68, -119, -238, and -476 

Prime Factorization of 476

The prime factorization of 476 is the way of expressing its prime factors in the product form.

Prime Factorization: 2 x 2 x 7 x 7

In this article, we will learn about the factors of 476 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 476?

The factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476. These numbers are the factors as they do not leave any remainder when divided by 476.

The factors of 476 are classified as prime numbers and composite numbers. The prime factors of the number 476 can be determined using the prime factorization technique.

How To Find the Factors of 476?

You can find the factors of 476 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 476, create a list containing the numbers that are exactly divisible by 476 with zero remainders. One important thing to note is that 1 and 476 are 476’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 476 are determined as follows:

\[\dfrac{476}{1} = 476\]

\[\dfrac{476}{2} = 238\]

\[\dfrac{476}{4} = 119\]

\[\dfrac{476}{7} = 68\]

\[\dfrac{476}{214} = 34\]

\[\dfrac{476}{17} = 8\]

Therefore, 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476 are the factors of 476.

Total Number of Factors of 476

For 476, there are twelve positive factors and twelve negative ones. So in total, there are twenty-four factors of 476. 

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 476 is given as:

Factorization of 476 is 1 x 2$^2$ x 7 x 17.

The exponent of 1, 7, and 17 is 1. The exponent of 2 is 2. 

Adding 1 to each and multiplying them together results in 24.

Therefore, the total number of factors of 476 is 24. Twelve are positive, and twelve 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 476 by Prime Factorization

The number 476 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 476 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 476, 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 476 can be expressed as:

476 = 2 x 2 x 7 x 17

Factors of 476 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 476, the factor pairs can be found as:

1 x 476 = 476

2 x 238 = 476 

4 x 119 = 476 

7 x 68 = 476 

14 x 34 = 476 

17 x 28 = 476 

The possible factor pairs of 476 are given as (1, 476), (2, 238), (4, 119), (7, 68), (14, 34), and (17, 28).

All these numbers in pairs, when multiplied, give 476 as the product.

The negative factor pairs of 476 are given as:

-1 x -476 = 476

-2 x -238 = 476 

-4 x -119 = 476 

-7 x -68 = 476 

-14 x -34 = 476 

-17 x -28 = 476 

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, -7, -14, -17, -28, -34, -68, -119, -238, and -476  are called negative factors of 476.

Factors of 476 Solved Examples

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

Example 1

How many factors of 476 are there?

Solution

The total number of Factors of 476 is 12.

Factors of 476 are 1, 2, 4, 7, 14, 17, 28, 34, 68, 119, 238, and 476. 

Example 2

Find the factors of 476 using prime factorization.

Solution

The prime factorization of 476 is given as:

476 $\div$ 2 = 238 

238 $\div$ 2 = 129 

129 $\div$ 7 = 17 

17 $\div$ 17 = 1 

So the prime factorization of 476 can be written as:

2 x 2 x 7 x 17  = 476

Factors of 475|Factors List| Factors of 477