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Factors of 304: Prime Factorization, Methods, and Examples
The factors of 304 are the numbers that result in zero as the remainder when 304 acts as the dividend for such numbers.
The given number’s factors can be positive and negative, provided that the given number is achieved upon multiplication of two-factor integers.
Factors of 304
Here are the factors of number 304.
Factors of 304: 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304
Negative Factors of 304
The negative factors of 304 are similar to its positive aspects, just with a negative sign.
Negative Factors of 304: -1, -2, -4, -8, -16, -19, -38, -76, -152, and -304
Prime Factorization of 304
The prime factorization of 304 is the way of expressing its prime factors in the product form.
Prime Factorization: $2^{4}$ x 19
In this article, we will learn about the factors of 304 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 304?
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304. These numbers are the factors as they do not leave any remainder when divided by 304.
The factors of 304 are classified as prime numbers and composite numbers. The prime factors of the number 304 can be determined using the prime factorization technique.
How To Find the Factors of 304?
You can find the factors of 304 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 304, create a list containing the numbers that are exactly divisible by 304 with zero remainders. One important thing to note is that 1 and 304 are the 304’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 304 are determined as follows:
\[\dfrac{304}{1} = 304\]
\[\dfrac{304}{2} = 152\]
\[\dfrac{304}{4} = 76\]
\[\dfrac{304}{8} = 38\]
\[\dfrac{304}{16} = 19\]
Therefore, 1, 2, 4, 8, 16, and the respective quotients 19, 38, 76, 152, and 304 are the factors of 304.
Total Number of Factors of 304
For 304, there are 10 positive factors and 10 negative ones. So in total, there are 20 factors of 304.
To find the total number of factors of the given number, follow the procedure mentioned below:
- Find the 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 304 is given as:
Factorization of 304 is 1 x $2^{4}$ x 19.
The exponent of 1 and 19 is 1 and that of 2 is 4.
Adding 1 to each and multiplying them together results in 20.
Therefore, the total number of factors of 304 is 20. 10 is positive, and 10 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 304 by Prime Factorization
The number 304 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 304 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 304, 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 304 can be expressed as:
304 = $2^{4}$ x 19
Factors of 304 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 304, the factor pairs can be found as:
1 x 304 = 304
2 x 152 = 304
4 x 76 = 304
8 x 38 = 304
16 x 19 = 304
The possible factor pairs of 304 are given as (1, 304), (2, 152), (4, 76), (8, 38), and (16, 19).
All these numbers in pairs, when multiplied, give 304 as the product.
The negative factor pairs of 304 are given as:
-1 x -304 = 304
-2 x -152 = 304
-4 x -76 = 304
-8 x -38 = 304
-16 x -19 = 304
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, -16, -19, -38, -76, -152, and -304 are called negative factors of 304.
The list of all the factors of 304, including positive as well as negative numbers, is given below.
Factor list of 304: 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 19, -19, 38, -38, 76, -76, 152, -152, 304, and -304
Factors of 304 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 304 are there?
Solution
The total number of Factors of 304 is 10.
Factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, and 304.
Example 2
Find the factors of 304 using prime factorization.
Solution
The prime factorization of 304 is given as:
304 $\div$ 2 = 152
152 $\div$ 2 = 76
76 $\div$ 2 = 38
38 $\div$ 2 = 19
19 $\div$ 19 = 1
So the prime factorization of 304 can be written as:
$2^{4}$ x 19 = 304