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Factors of 480: Prime Factorization, Methods, and Examples
The factors of 480 are the listings of numbers that when divided by 480 leave nothing as remainders. The factors of 480 can be positive and negative.
The number 480 is an even number and also a composite number.
Factors of 480
Here are the factors of number 480.
Factors of 480: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, and 480
Negative Factors of 480
The negative factors of 480 are similar to their positive aspects, just with a negative sign.
Negative Factors of 480: –1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -80, -96, -120, -160, -240, and -480
Prime Factorization of 480
The prime factorization of 480 is the way of expressing its prime factors in the product form.
Prime Factorization: 2$^5$ x 3 x 5
In this article, we will learn about the factors of 480 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 480?
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, and 480. These numbers are the factors as they do not leave any remainder when divided by 480.
The factors of 480 are classified as prime numbers and composite numbers. The prime factors of the number 480 can be determined using the prime factorization technique.
How To Find the Factors of 480?
You can find the factors of 480 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 480, create a list containing the numbers that are exactly divisible by 480 with zero remainders. One important thing to note is that 1 and 480 are 480’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 480 are determined as follows:
\[\dfrac{480}{1} = 480\]
\[\dfrac{480}{2} = 240\]
\[\dfrac{480}{3} = 160\]
\[\dfrac{480}{4} = 120\]
\[\dfrac{480}{5} = 96\]
\[\dfrac{480}{8} = 80\]
\[\dfrac{480}{10} = 48\]
\[\dfrac{480}{12} = 40\]
\[\dfrac{480}{15} = 32\]
\[\dfrac{480}{16} = 30\]
\[\dfrac{480}{20} = 24\]
Therefore, 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, and 480 are the factors of 480.
Total Number of Factors of 480
For 480, there are 24 positive factors and 24 negative ones. So in total, there are 48 factors of 480.
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 480 is given as:
Factorization of 480 is 1 x 2$^5$ x 3 x 5.
The exponent of 1, 3, and 5 is 1. The exponent of 2 is 5.
Adding 1 to each and multiplying them together results in 48.
Therefore, the total number of factors of 480 is 48. Twenty-four are positive, and twenty-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 480 by Prime Factorization
The number 480 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 480 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 480, 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 480 can be expressed as:
480 = 2$^5$ x 3 x 5
Factors of 480 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 480, the factor pairs can be found as:
1 x 480 = 480
2 x 240 = 480
3 x 160 = 480
4 x 120 = 480
5 x 96 = 480
6 x 80 = 480
8 x 60 = 480
10 x 48 = 480
12 x 40 = 480
15 x 32 = 480
16 x 30 = 480
20 x 24 = 480
The possible factor pairs of 480 are given as (1, 480), (2, 240), (3, 160), (4, 120), (5, 96), (6, 80), (8, 60), (10, 48), (12, 40), (15, 32), (16, 30), and (20, 24).
All these numbers in pairs, when multiplied, give 480 as the product.
The negative factor pairs of 480 are given as:
-1 x -480 = 480
-2 x -240 = 480
-3 x -160 = 480
-4 x -120 = 480
-5 x -96 = 480
-6 x -80 = 480
-8 x -60 = 480
-10 x -48 = 480
-12 x -40 = 480
-15 x -32 = 480
-16 x -30 = 480
-20 x -24 = 480
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, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -32, -40, -48, -60, -80, -96, -120, -160, -240, and -480 are called negative factors of 480.
The list of all the factors of 480, including positive as well as negative numbers, is given below.
Factor list of 480: 1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 8, -8, 10, -10, 12, -12, 15, -15, 16, -16, 20, -20, 24, -24, 30, -30, 32, -32, 40, -40, 48, -48, 60, -60, 80, -80, 96, -96, 120, -120, 160, -160, 240, -240, 480, and -480
Factors of 480 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 480 are there?
Solution
The total number of Factors of 480 is twenty-four.
Factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, and 480.
Example 2
Find the factors of 480 using prime factorization.
Solution
The prime factorization of 480 is given as:
480 $\div$ 2 = 240
240 $\div$ 2 = 120
120 $\div$ 2 = 60
60 $\div$ 2 = 30
30 $\div$ 2 = 15
15 $\div$ 3 = 5
5 $\div$ 5 = 1
So the prime factorization of 480 can be written as:
2$^5$ x 3 x 5 = 480