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Factors of 139: Prime Factorization, Methods, and Examples
The factors of 139 are the numbers that completely divide 139 and leave zero as the remainder behind or a whole number quotient.
Since the number 139, is a prime number, it only consists of two factors. These factors are the number 1 and the number itself, which is 139.
Factors of 139
Here are the factors of the number 139.
Factors of 139: 1 and 139
Negative Factors of 139
The negative factors of 139 are similar to its positive factors, just with a negative sign.
Negative Factors of 139: -1 and -139
Prime Factorization of 139
The prime factorization of 139 is the way of expressing its prime factors in the product form.
Prime Factorization: 1 x 139
In this article, we will learn about the factors of 139 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 139?
The factors of 139 are 1 and 139. All of these numbers are the factors as they do not leave any remainder when divided by 139.
The factors of 139 are classified as prime numbers and composite numbers. The prime factors of the number 139 can be determined using the technique of prime factorization.
How To Find the Factors of 139?
You can find the factors of 139 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 139, create a list containing the numbers that are exactly divisible by 139 with zero remainders. One important thing to note is that 1 and 139 are the 139’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 139 are determined as follows:
\[\dfrac{139}{1} = 139\]
\[\dfrac{139}{139} = 1\]
Therefore, 1 and 139 are the factors of 139.
Total Number of Factors of 139
For 139 there are 2 positive factors and 2 negative ones. So in total, there are 4 factors of 139.
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 139 is given as:
Factorization of 139 is 1 x 139.
The exponent of 1 and 139 is 1.
Adding 1 to each and multiplying them together results in 4.
Therefore, the total number of factors of 139 is 4, where 2 are positive factors and 2 are negative factors.
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 139 by Prime Factorization
The number 139 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 139 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 139, 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 139 can be expressed as:
139 = 1 x 139
Factors of 139 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 139, the factor pairs can be found as:
1 x 139 = 139
The possible factor pair of 139 is given as (1, 139).
All these numbers in pairs, when multiplied, give 139 as the product.
The negative factor pairs of 139 are given as:
-1 x -139 = 139
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 -139 are called negative factors of 139.
The list of all the factors of 139 including positive as well as negative numbers is given below.
Factor list of 139: 1, -1, 139, and -139
Factors of 139 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 139 are there?
Solution
The total number of Factors of 139 is 2.
Factors of 139 are 1 and 139.
Example 2
Find the factors of 139 using prime factorization.
Solution
The prime factorization of 139 is given as:
139 $\div$ 139 = 1
So the prime factorization of 139 can be written as:
1 x 139 = 139