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Factors of 293: Prime Factorization, Methods, and Examples
The factors of 293 are the numbers that can divide 293 entirely without remainder. The number 293 is an odd number. It is also a prime number which indicates that it has only two factors; 1 and 293.
The factors of the number can be positive and negative integers.
Factors of 293
Here are the factors of number 293.
Factors of 293: 1 and 293
Negative Factors of 293
The negative factors of 293 are similar to its positive factors, just with a negative sign.
Negative Factors of 293: -1 and -293
Prime Factorization of 293
The prime factorization of 293 is the way of expressing its prime factors in the product form.
Prime Factorization: 1 x 293
In this article, we will learn about the factors of 293 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 293?
The factors of 293 are 1 and 293. All of these numbers are the factors as they do not leave any remainder when divided by 293.
The factors of 293 are classified as prime numbers and composite numbers. The prime factors of the number 293 can be determined using the technique of prime factorization.
How To Find the Factors of 293?
You can find the factors of 293 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 293, create a list containing the numbers that are exactly divisible by 293 with zero remainders. One important thing to note is that 1 and 293 are the 293’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 293 are determined as follows:
\[\dfrac{293}{1} = 293\]
Therefore, 1 and 293 are the factors of 293.
Total Number of Factors of 293
For 293 there are two positive factors and two negative ones. So in total, there are four factors of 293.
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 293 is given as:
Factorization of 293 is 1 x 293
The exponent of 1 and 293 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 293 is four. Two are positive and two factors are negative.
Important Notes
Here are some important 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 293 by Prime Factorization
The number 293 is a prime number. Prime factorization is a useful technique for finding the number’s prime factors and expressing the number as the product of its prime factors.
Before finding the factors of 293 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 293, start dividing by its smallest 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 293 can be expressed as:
293 = 1 x 293
Factors of 293 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 of the given numbers.
For 293, the factor pairs can be found as:
1 x 293 = 293
The possible factor pair of 293 is given as (1, 293).
All these numbers in pairs, when multiplied, give 293 as the product.
The negative factor pairs of 293 are given as:
-1 x -293 = 293
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 -293 are called negative factors of 293.
The list of all the factors of 293, including positive as well as negative numbers is given below.
Factor list of 293: 1, -2, 293, and -293
Factors of 293 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 293 are there?
Solution
The total number of Factors of 293 is two.
Factors of 293 are 1 and 293.
Example 2
Find the factors of 293 using prime factorization.
Solution
The prime factorization of 293 is given as:
293 $\div$ 1 = 293
So the prime factorization of 293 can be written as:
1 x 293 = 293