JUMP TO TOPIC
Factors of 185: Prime Factorization, Methods, and Examples
The factors of 185 are numbers that when divided by 185 leave zero as the remainder. This means the numbers that completely divide the given number are named as its factors.
The factors of the given number can be positive as well as negative provided that the given number is achieved upon multiplication of two-factor integers.
Factors of 185
Here are the factors of number 185.
Factors of 185: 1, 5, 37, 185
Negative Factors of 185
The negative factors of 185 are similar to its positive factors, just with a negative sign.
Negative Factors of 185: – 1, -5, -37, -185
Prime Factorization of 185
The prime factorization of 185 is the way of expressing its prime factors in the product form.
Prime Factorization: 5 x 37
In this article, we will learn about the factors of 185 and how to find them using various techniques such as upside-down division, prime factorization, and factor tree.
What Are the Factors of 185?
The factors of 185 are 1, 5, 37, and 185. All of these numbers are the factors as they do not leave any remainder when divided by 185.
The factors of 185 are classified as prime numbers and composite numbers. The prime factors of the number 185 can be determined using the technique of prime factorization.
How To Find the Factors of 185?
You can find the factors of 185 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 185, create a list containing the numbers that are exactly divisible by 185 with zero remainders. One important thing to note is that 1 and 185 are the 185’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 185 are determined as follows:
\[\dfrac{185}{1} = 185\]
\[\dfrac{185}{5} = 37\]
\[\dfrac{185}{185} = 1\]
Therefore, 1, 5, 37, and 185 are the factors of 185.
Total Number of Factors of 185
For 185 there are 4 positive factors and 4 negative ones. So in total, there are 8 factors of 185.
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 185 is given as:
Factorization of 185 is 1 x 5 x 37.
The exponent of 1, 5, and 37 is 1.
Adding 1 to each and multiplying them together results in 8.
Therefore, the total number of factors of 185 is 8. 4 are positive and 4 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 185 by Prime Factorization
The number 185 is a 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 185 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 185, 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 185 can be expressed as:
\[ 185 = 5 \times 37 \]
Factors of 185 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 185, the factor pairs can be found as:
\[ 1 \times 185 = 185 \]
\[ 5 \times 37 = 185 \]
The possible factor pairs of 185 are given as (1, 185) and (5, 37 ).
All these numbers in pairs, when multiplied, give 185 as the product.
The negative factor pairs of 185 are given as:
\[ -1 \times -185 = 185 \]
\[ -5 \times -37 = 185 \]
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, -5, -37, and -185 are called negative factors of 185.
The list of all the factors of 185 including positive as well as negative numbers is given below.
Factor list of 185: 1, -1, 5, -5, 37, -37, 185, and -185
Factors of 185 Solved Examples
To better understand the concept of factors, let’s solve some examples.
Example 1
How many factors of 185 are there?
Solution
The total number of Factors of 185 is 4.
Factors of 185 are 1, 5, 37, and 185.
Example 2
Find the factors of 185 using prime factorization.
Solution
The prime factorization of 185 is given as:
\[ 185 \div 5 = 37 \]
\[ 37 \div 37 = 1 \]
So the prime factorization of 185 can be written as:
\[ 5 \times 37 = 185 \]