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Factors of 102: Prime Factorization, Methods, and Examples
The factors of 102 are the numbers that generate zero as a remainder and a whole number quotient when 102 is divided from such numbers. For such numbers, both the divisors and the quotients act as factors.
The number 102 is even composite so that automatically means that this number, 102, has multiple factors. And since 102 is an even number as well, so the number 2 is one of the factors of 102. Let’s take a look at factors of 102 and how to determine them.
Factors of 102
Here are the factors of number 102.
Factors of 102: 1, 2, 3, 6, 17, 34, 51, and 102
Negative Factors of 102
The negative factors of 102 are similar to its positive factors, just with a negative sign.
Negative Factors of 102: -1, -2, -3, -6, -17, -34, -51 and -102
Prime Factorization of 102
The prime factorization of 102 is the product of its prime factors.
Prime Factorization: 2 x 3 x 17
In this article, we will learn about the factors of 102 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 102?
The factors 102 are 1, 2, 3, 6, 17, 34, 51, and 102. All of these numbers are the factors as they do not leave any remainder when 102 is divided by them.
The factors of 102 are classified as prime numbers and composite numbers. The prime factors of the number 102 can be determined using the technique of prime factorization.
How To Find the Factors of 102?
You can find the factors of 102 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 102, create a list containing the numbers that are exactly divisible by 102 with zero remainders. One important thing to note is that 1 and 102 are the 102’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 102 are determined as follows:
\[\dfrac{102}{1} = 102\]
\[\dfrac{102}{2} = 51\]
\[\dfrac{102}{3} = 34\]
\[\dfrac{102}{6} = 17\]
\[ \dfrac{102}{17} = 6\]
\[ \dfrac{102}{34} = 3\]
\[ \dfrac{102}{51} = 2\]
\[ \dfrac{102}{102} =1\]
Therefore, 1, 2, 3, 6, 17, 34, 51, and 102 are the factors of 102.
Total Number of Factors of 102
For 102 there are 8 positive factors and 8 negative ones. So in total, there are 8 factors of 102.
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 102 is given as:
Factorization of 102 is 1 x 2 x 3 x 17.
The exponent for all of them is 1.
Adding 1 to each and multiplying them together results in 16.
Therefore, the total number of factors of 102 is 16.
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 102 by Prime Factorization
The number 102 is a composite 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 102 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 102, 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 102 can be expressed as:
102 = 2 x 3 x 17
Factors of 102 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 102, the factor pairs can be found as:
2 x 51 = 102
3 x 34 = 102
6 x 17 = 102
1 x 102 = 102
The possible factor pairs of 102 are given as (1, 102), (2, 51), (3, 34), and (6, 17 ).
All these numbers in pairs, when multiplied, give 102 as the product.
The negative factor pairs of 102 are given as:
-1 x -102 = 102
-2 x -51 = 102
-3 x -34 = 102
-6 x -17 = 102
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, -2, -3, -6, -17, -34 and -51 are called negative factors of 102.
The list of all the factors of 102 including positive as well as negative numbers is given below.
Factor list of 102: 1, -1, 2, -2, 3, -3, 6, -6, -17, 17, 34, -34, 51, -51, 102, and -102
Factors of 102 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 102 are there?
Solution
The total number of Factors of 102 is 8.
Factors of X are 1, 2, 3, 6, 17, 34, 51, and 102.
Example 2
Find the factors of 102 using prime factorization.
Solution
The prime factorization of 102 is given as:
102 $\div$ 2 = 51
51 $\div$ 3 = 17
17 $\div$ 17 = 1
So the prime factorization of 102 can be written as:
2 x 3 x 17= 102