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Factors of 197: Prime Factorization, Methods, and Examples
The factors of 197 are the numbers that produce zero as the remainder. These factors can be both positive and negative. These factors are the same with the exception that the signs are reversed.
Since the number 197 is a prime number, so it only has 2 factors.
Factors of 197
Here are the factors of number 197.
Factors of 197: 1, 197
Negative Factors of 197
The negative factors of 197 are similar to its positive factors, just with a negative sign.
Negative Factors of 197: -1, -197
Prime Factorization of 197
The prime factorization of 197 is the way of expressing its prime factors in the product form.
Prime Factorization: 1 x 197
In this article, we will learn about the factors of 197 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 197?
The factors of 197 are 1 and 197. All of these numbers are the factors as they do not leave any remainder when divided by 197.
The factors of 197 are classified as prime numbers. The prime factors of the number 197 can be determined using the technique of prime factorization.
How To Find the Factors of 197?
You can find the factors of 197 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 197, create a list containing the numbers that are exactly divisible by 197 with zero remainders. One important thing to note is that 1 and 197 are the 197’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 197 are determined as follows:
\[\dfrac{197}{1} = 197\]
\[\dfrac{197}{197} = 1\]
Therefore, 1 and 197 are the factors of 197.
Total Number of Factors of 197
For 197 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 197.
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 197 is given as:
Factorization of 197 is 1 x 197.
The exponent of 1 and 197 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 197 is 4. 2 are positive and 2 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 197 by Prime Factorization
The number 197 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 197 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 197, 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 197 can be expressed as:
197 = 1 x 197
Factors of 197 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 197, the factor pairs can be found as:
1 x 197 = 197
The possible factor pair of 197 is given as (1, 197).
All these numbers in pairs, when multiplied, give 197 as the product.
The negative factor pairs of 197 are given as:
-1 x -197 = 197
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 -197 are called negative factors of 197.
The list of all the factors of 197 including positive as well as negative numbers is given below.
Factor list of 197: 1, -1, 197, and -197
Factors of 197 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 197 are there?
Solution
The total number of Factors of 197 is 2.
Factors of 197 are 1 and 197.
Example 2
Find the factors of 197 using prime factorization.
Solution
The prime factorization of 197 is given as:
197 $\div$ 197 = 1
So the prime factorization of 197 can be written as:
1 x 197 = 197