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Factors of 838: Prime Factorization, Methods, and Examples
The number 838 is a positive composite number. the term positive means that the number is greater than zero whereas, by composite, we mean that the number has more than 2 factors.
The number of factors of 838 is 4 which makes a total of 2-factor pairs.
Factors of 838
Here are the factors of number 838.
Factors of 838: 1, 2, 419, and 838
Negative Factors of 838
The negative factors of 838 are similar to its positive aspects, just with a negative sign.
Negative Factors of 838: -1, -2, -419, and -838
Prime Factorization of 838
The prime factorization of 838 is the way of expressing its prime factors in the product form.
Prime Factorization: 2 x 419
In this article, we will learn about the factors of 838 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 838?
The factors of 838 are 1, 2, 419, and 838. These numbers are the factors as they do not leave any remainder when divided by 838.
The factors of 838 are classified as prime numbers and composite numbers. The prime factors of the number 838 can be determined using the prime factorization technique.
How To Find the Factors of 838?
You can find the factors of 838 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 838, create a list containing the numbers that are exactly divisible by 838 with zero remainders. One important thing to note is that 1 and 838 are the 838’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 838 are determined as follows:
\[\dfrac{838}{1} = 838\]
\[\dfrac{838}{2} = 419\]
\[\dfrac{838}{419} = 2\]
\[\dfrac{838}{838} = 1\]
Therefore, 1, 2, 419, and 838 are the factors of 838.
Total Number of Factors of 838
For 838, there are 4 positive factors and 4 negative ones. So in total, there are m factors of 838.
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 838 is given as:
Factorization of 838 is 1 x 2 x 419.
The exponent of 1, 2, and 419 is 1.
Adding 1 to each and multiplying them together results in m.
Therefore, the total number of factors of 419 is 8. 4 are positive, and 4 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 838 by Prime Factorization
The number 838 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 838 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 838, 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 838 can be expressed as:
838 = 2 x 419
Factors of 838 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 838, the factor pairs can be found as:
1 x 838 = 838
2 x 419 = 838
The possible factor pairs of 838 are given as (1, 838) and (2, 419).
All these numbers in pairs, when multiplied, give 838 as the product.
The negative factor pairs of 838 are given as:
-1 x -838 = 838
-2 x -419 = 838
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, -419, and -838 are called negative factors of 838.
The list of all the factors of 838, including positive as well as negative numbers, is given below.
Factor list of 838: 1, -1, 2, -2, 419, -419, 838, and -838
Factors of 838 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 838 are there?
Solution
The total number of Factors of 838 is 4.
Factors of 838 are 1, 2, 419, and 838.
Example 2
Find the factors of 838 using prime factorization.
Solution
The prime factorization of 838 is given as:
838 $\div$ 2 = 419
419 $\div$ 419 = 1
So the prime factorization of 838 can be written as:
2 x 419 = 838