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Factors of 481: Prime Factorization, Methods, and Examples
The factors of 481 are numbers that, when multiplied in pairs, resulting in 481. The factors of 481 can be positive and negative. The factors of 481 can be determined using the division method.
Another important method that we will be discussing in this lesson is prime factorization.
Factors of 481
Here are the factors of number 481.
Factors of 481: 1, 13, 37, and 481
Negative Factors of 481
The negative factors of 481 are similar to their positive aspects, just with a negative sign.
Negative Factors of 481: –1, -13, -37, and -481
Prime Factorization of 481
The prime factorization of 481 is the way of expressing its prime factors in the product form.
Prime Factorization: 13 x 37
In this article, we will learn about the factors of 481 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 481?
The factors of 481 are 1, 13, 37, and 481. These numbers are the factors as they do not leave any remainder when divided by 481.
The factors of 481 are classified as prime numbers and composite numbers. The prime factors of the number 481 can be determined using the prime factorization technique.
How To Find the Factors of 481?
You can find the factors of 481 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 481, create a list containing the numbers that are exactly divisible by 481 with zero remainders. One important thing to note is that 1 and 481 are 481’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 481 are determined as follows:
\[\dfrac{481}{1} = 481\]
\[\dfrac{481}{13} = 37\]
Therefore, 1, 13, 37, and 481 are the factors of 481.
Total Number of Factors of 481
For 481, there are four positive factors and four negative ones. So in total, there are eight factors of 481.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the factorization/prime factorization of the given number.
- Demonstrate the prime factorization of the number in the form of exponent form.
- Add 1 to each of the exponents of the prime factor.
- 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 481 is given as:
Factorization of 481 is 1 x 13 x 37.
The exponent of 1, 13, and 37 is 1.
Adding 1 to each and multiplying them together results in eight.
Therefore, the total number of factors of 481 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 481 by Prime Factorization
The number 481 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 481 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 481, 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 481 can be expressed as:
481 = 13 x 37
Factors of 481 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 481, the factor pairs can be found as:
1 x 481 = 481
13 x 37 = 481
The possible factor pairs of 481 are given as (1, 481) and (13, 37).
All these numbers in pairs, when multiplied, give 481 as the product.
The negative factor pairs of 481 are given as:
-1 x -481 = 481
-13 x -37 = 481
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, -13, -37, and -481 are called negative factors of 481.
The list of all the factors of 481, including positive as well as negative numbers, is given below.
Factor list of 481: 1, -1, 13, -13, 37, -37, 481, and -481
Factors of 481 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 481 are there?
Solution
The total number of Factors of 481 is four.
Factors of 481 are 1, 13, 37, and 481.
Example 2
Find the factors of 481 using prime factorization.
Solution
The prime factorization of 481 is given as:
481 $\div$ 13 = 37
37 $\div$ 37 = 1
So the prime factorization of 481 can be written as:
13 x 37 = 481