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Factors of 438: Prime Factorization, Methods, and Examples
The factors of 438 are the integers that, when divided by 438, leave nothing as a remainder. There are eight factors of 438, which indicates that it is a composite number. The factors of 438 can be positive or negative.
We will find out more about the factors in the article.
Factors of 438
Here are the factors of number 438.
Factors of 438: 1, 2, 3, 6, 73, 146, 219, and 438.
Negative Factors of 438
The negative factors of 438 are similar to their positive aspects, just with a negative sign.
Negative Factors of 438: –1, -2, -3, -6, -73, -146, -219, and -438.
Prime Factorization of 438
The prime factorization of 438 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 3 x 73
In this article, we will learn about the factors of 438 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 438?
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, and 438. These numbers are the factors as they do not leave any remainder when divided by 438.
The factors of 438 are classified as prime numbers and composite numbers. The prime factors of the number 438 can be determined using the prime factorization technique.
How To Find the Factors of 438?
You can find the factors of 438 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 438, create a list containing the numbers divisible by 438 with zero remainders. One important thing to note is that 1 and 438 are the 438’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 438 are determined as follows:
\[\dfrac{438}{1} = 438\]
\[\dfrac{438}{2} = 219\]
\[\dfrac{438}{3} = 146\]
\[\dfrac{438}{6} = 73\]
Therefore, 1, 2, 3, 6, 73, 146, 219, and 438 are the factors of 438.
Total Number of Factors of 438
For 438, there are Eight positive factors and Eight negative ones. So in total, there are 16 factors of 438.
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 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 438 is given as:
Factorization of 438 is 1 x 2 x 3 x 73 .
The exponent of 1, 2, 3, and 73 is 1.
Adding 1 to each and multiplying them together results in m.
Therefore, the total number of factors of 438 is 16. Eight are positive, and eight 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 number factors 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 two as its prime factor, the smallest prime factor.
Factors of 438 by Prime Factorization
The number 438 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 438 using prime factorization, let us determine 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 438, divide 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 438 can be expressed as:
438 = 2 x 3 x 73
Factors of 438 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.
For X, the factor pairs can be found as:
1 x 438 = 438
2 x 219 = 438
3 x 146 = 438
6 x 73 = 438
The possible factor pairs of 438 are given as (1, 438), (2, 219), (3, 146), and (6, 73 ).
All these numbers in pairs, when multiplied, give 438 as the product.
The negative factor pairs of 438 are given as:
-1 x -438 = 438
-2 x -219 = 438
-3 x -146 = 438
-6 x -73 = 438
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, -6, -73, -146, -219, and -438 are called negative factors of 438.
The list of all the factors of 438, including positive and negative numbers, is given below.
Factor list of 438: –1, -2, -3, -6, -73, -146, -219, and -438.
Factors of 438 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 438 are there?
Solution
The total number of Factors of 438 is 16.
Factors of 438 are 1, 2, 3, 6, 73, 146, 219, and 438.
Example 2
Find the factors of 438 using prime factorization.
Solution
The prime factorization of 438 is given as:
438 $\div$ 2 = 219
219 $\div$ 3 = 73
73 $\div$ 73 = 1
So the prime factorization of 438 can be written as:
2 x 3 x 73 = 438