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Factors of 117: Prime Factorization, Methods, and Examples
The factors of 117 are the numbers that give off zero as a reminder when 117 is divided by such numbers. In other words, these are the numbers upon which the number 117 is completely divisible.
There are multiple factors of 117 as the number 117 is an odd composite number. These factors can be determined through techniques such as the division technique and the prime factorization technique.
Factors of 117
Here are the factors of number 117.
Factors of 117: 1, 3, 9, 13, 39, 117
Negative Factors of 117
The negative factors of 117 are similar to its positive factors, just with a negative sign.
Negative Factors of 117: -1, -3, -9, -13, -39 and -117
Prime Factorization of 117
The prime factorization of 117 is the product of 117 expressed in terms of its prime factors.
Prime Factorization: 3 x 3 x 13
In this article, we will learn about the factors of 117 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 117?
The factors of 117 are 1, 3, 9, 13, 39, and 117. All of these numbers are the factors as they do not leave any remainder when divided by 117.
The factors of 117 are classified as prime numbers and composite numbers. The prime factors of the number 117 can be determined using the technique of prime factorization.
How To Find the Factors of 117?
You can find the factors of 117 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 117, create a list containing the numbers that are exactly divisible by 117 with zero remainders. One important thing to note is that 1 and 117 are the 117’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 117 are determined as follows:
\[\dfrac{117}{1} = 117\]
\[\dfrac{117}{3} = 39\]
\[\dfrac{117}{9} = 13\]
\[\dfrac{117}{13} = 9\]
\[ \dfrac{117}{39} = 3 \]
\[ \dfrac{117}{117} = 1\]
Therefore, 1, 3, 9, 13, 39, and 117 are the factors of 117.
Total Number of Factors of 117
For 117 there are 6 positive factors and 6 negative ones. So in total, there are 12 factors of 117.
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 117 is given as:
Factorization of 117 is 1 x 3$^{2}$ x 13.
The exponent of 1 and 13 is 1 whereas that of 3 is 2.
Adding 1 to each and multiplying them together results in 12.
Therefore, the total number of factors of 117 is 12, where 6 are positive factors and 6 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 which is the smallest prime factor.
Factors of 117 by Prime Factorization
The number 117 is composite. 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 117 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 117, 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 117 can be expressed as:
117 = 3 x 3 x 13
Factors of 117 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.
For 117, the factor pairs can be found as:
1 x 117 = 117
3 x 39 = 117
13 x 9 = 117
The possible factor pairs of 117 are given as (1, 117), (3, 39), and(9, 13).
All these numbers in pairs, when multiplied, give 117 as the product.
The negative factor pairs of 117 are given as:
-1 x -117 = 117
-3 x -39 = 117
-9 x -13 = 117
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, -3, -9, -13, -39, and -117 are called negative factors of 117.
The list of all the factors of 117 including positive as well as negative numbers is given below
Factor list of 117: 1, -1, 3, -3, 9, -9, 13, -13, 39, -39, 117, and -117
Factors of 117 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 117 are there?
Solution
The total number of Factors of 117 is 6.
Factors of 117 are 1, 3, 9, 13, 39, and 117.
Example 2
Find the factors of 117 using prime factorization.
Solution
The prime factorization of 117 is given as:
117 $\div$ 3 = 39
39 $\div$ 3 = 13
13 $\div$ 13 =1
So the prime factorization of 117 can be written as:
3 x 3 x 13 = 117