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Factors of 311: Prime Factorization, Methods, and Examples
The factors of 311 are defined as the numbers that are divisible by 311. The number 311 is an odd number. It is also a prime number which is why it has only two factors.
Let’s find out more about the factors of 311.
Factors of 311
Here are the factors of number 311.
Factors of 311: 1 and 311
Negative Factors of 311
The negative factors of 311 are similar to its positive aspects, just with a negative sign.
Negative Factors of 311: -1 and -311
Prime Factorization of 311
The prime factorization of 311 is the way of expressing its prime factors in the product form.
Prime Factorization: 1 x 311
In this article, we will learn about the factors of 311 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 311?
The factors of 311 are 1 and 311. These numbers are the factors as they do not leave any remainder when divided by 311.
The factors of 311 are classified as prime numbers and composite numbers. The prime factors of the number 311 can be determined using the prime factorization technique.
How To Find the Factors of 311?
You can find the factors of 311 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 311, create a list containing the numbers that are exactly divisible by 311 with zero remainders. One important thing to note is that 1 and 311 are 311’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 311 are determined as follows:
\[\dfrac{311}{1} = 311\]
Therefore, 1 and 311 are the factors of 311.
Total Number of Factors of 311
For 311, there are two positive factors and two negative ones. So in total, there are four factors of 311.
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 311 is given as:
Factorization of 311 is 1 x 311.
The exponent of 1 and 311 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 311 is four. Two are positive, and two 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 311 by Prime Factorization
The number 311 is a prime 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 311 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 311, 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 311 can be expressed as:
311 = 1 x 311
Factors of 311 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 311, the factor pairs can be found as:
1 x 311 = 311
The possible factor pairs of 311 are given as (1, 311).
All these numbers in pairs, when multiplied, give 311 as the product.
The negative factor pairs of 311 are given as:
-1 x -311 = 311
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 and -311 are called negative factors of 311.
The list of all the factors of 311, including positive as well as negative numbers, is given below.
Factor list of 311: 1, -1, 311, and -311
Factors of 311 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 311 are there?
Solution
The total number of Factors of 311 is two.
Factors of 311 are 1 and 311.
Example 2
Find the factors of 311 using prime factorization.
Solution
The prime factorization of 311 is given as:
311 $\div$ 1 = 311
So the prime factorization of 311 can be written as:
1 x 311 = 311