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Factors of 97: Prime Factorization, Methods, and Examples

The factors of 97 are defined as the whole numbers that are completely divided by 97 also when found in pairs their multiplication results in 97. It is an odd prime number so it has only two factors due to its prime nature.

The factors of the given number can be positive and negative provided that the product of any of those two is always the factored number.

Factors of 97

Here are the factors of number 97.

Factors of 97: 1 and 97

Negative Factors of 97

The negative factors of 97 are similar to its positive factors, just with a negative sign.

Negative Factors of 97: -1 and -97

Prime Factorization of 97

The prime factorization of 97 is the way of expressing a number’s prime factors in the form of its product.

Prime Factorization: 1 x 97

In this article, we will learn about the factors of 97 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.

What Are the Factors of 97?

The factors of 97 are 1 and 97 itself. Both of these numbers are the factors as they do not leave any remainder when divided by 97.

The factors of 97 are classified as 1 and 97 as 97 is a prime number. The prime factors of any number can be determined using the technique of prime factorization.

How To Find the Factors of 97?

You can find the factors of 97 by using the rules of divisibility. The rule of divisibility states that any number when divided by any other natural number then it 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 97, create a list containing the numbers that are exactly divisible by 97 with zero remainders. One important thing to note is that 1 and 97 are the 97’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 97 are determined as follows:

\[\dfrac{97}{1} = 97\]

\[\dfrac{97}{97} = 1\]

Therefore, 1 and 97 are the only factors of 97.

Total Number of Factors of 97

For 97 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 97. 

To find the total number of factors of the given number, follow the procedure mentioned below:

  1. Find the prime factorization of the given number.
  2. Demonstrate the prime factorization of the number in the form of exponent form.
  3. Add 1 to each of the exponents of the prime factor.
  4. 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 X is given as:

Factorization of 97 is 1 x 97.

The exponent of both 1 and 97 is 1.

Adding 1 to each and multiplying them together results in 4.

Therefore, the total number of factors of 97 is 4 of which 2 are positive and 2 negatives.

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 which is the smallest prime factor.

Factors of 97 by Prime Factorization

The number 97 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 97 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 97, 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 97 can be expressed as:

\[ 97 = 1 \times 97\]

Factors of 97 in Pairs

The factor pairs are the duplet of numbers that when multiplied together result in the factorized number. Depending upon the total number of factors of the given numbers, factor pairs can be more than one.

Since 97 is a prime number it has only one-factor pair that is (1, 97).

Both of these numbers in pairs, when multiplied, give 97 as the product.

The negative factor pairs of 97 can be written with a negative sign as (-1, -97).

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 -97 are called negative factors of 97.

The list of all the factors of 97 including positive as well as negative numbers is given below.

Factor list of 97: 1, -1, 97, and -97

Factors of 97 Solved Examples

To better understand the concept of factors, let’s solve some examples.

Example 1

How many factors of 97 are there?

Solution

The total number of Factors of 97 is 4.

Example 2

Find the sum of the factors of 97.

Solution

The sum of factors 97 can be obtained by adding all the factors.

Sum = 1+ 97 = 98

So the sum is equivalent to 98.

Factors of 96|Factors List |Factors of 98

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