103 LearnersLast updated on May 26th, 2025
Factors of 186
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 186, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 186?
The numbers that divide 186 evenly are known as factors of 186. A factor of 186 is a number that divides the number without remainder. The factors of 186 are 1, 2, 3, 6, 31, 62, 93, and 186.
Negative factors of 186: -1, -2, -3, -6, -31, -62, -93, and -186.
Prime factors of 186: 2, 3, and 31.
Prime factorization of 186: 2 × 3 × 31.
The sum of factors of 186: 1 + 2 + 3 + 6 + 31 + 62 + 93 + 186 = 384
How to Find Factors of 186?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 186. Identifying the numbers which are multiplied to get the number 186 is the multiplication method.
Step 1: Multiply 186 by 1, 186 × 1 = 186.
Step 2: Check for other numbers that give 186 after multiplying
2 × 93 = 186
3 × 62 = 186
6 × 31 = 186
Therefore, the positive factor pairs of 186 are: (1, 186), (2, 93), (3, 62), (6, 31). All these factor pairs result in 186. For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 186 by 1, 186 ÷ 1 = 186.
Step 2: Continue dividing 186 by the numbers until the remainder becomes 0.
186 ÷ 1 = 186
186 ÷ 2 = 93
186 ÷ 3 = 62
186 ÷ 6 = 31
Therefore, the factors of 186 are: 1, 2, 3, 6, 31, 62, 93, 186.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a prime number. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 186 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
186 ÷ 2 = 93
93 ÷ 3 = 31
31 ÷ 31 = 1
The prime factors of 186 are 2, 3, and 31. The prime factorization of 186 is: 2 × 3 × 31.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 186 is divided by 2 to get 93.
Step 2: Now divide 93 by 3 to get 31.
Step 3: Here, 31 is a prime number, that cannot be divided anymore. So, the prime factorization of 186 is: 2 × 3 × 31.
Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
- Positive factor pairs of 186: (1, 186), (2, 93), (3, 62), (6, 31).
- Negative factor pairs of 186: (-1, -186), (-2, -93), (-3, -62), (-6, -31).
Common Mistakes and How to Avoid Them in Factors of 186
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself. For example, in factors of 186, 1 and 186 are also factors.
Factors of 186 Examples
Problem 1
There are 93 students and 186 candies. How will they divide it equally?
They will get 2 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
186/93 = 2
Problem 2
A rectangular garden has a width of 31 meters and a total area of 186 square meters. Find the length?
6 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
186 = 31 × length
To find the value of the length, we need to shift 31 to the left side.
186/31 = length
Length = 6.
Problem 3
There are 62 boxes and 186 apples. How many apples will be in each box?
Each box will have 3 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
186/62 = 3
Problem 4
In a conference, there are 186 attendees, and 6 tables. How many attendees are there at each table?
There are 31 attendees at each table.
Explanation
Dividing the attendees with the total tables, we will get the number of attendees at each table.
186/6 = 31
Problem 5
186 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 62 books.
Explanation
Divide total books with shelves.
186/3 = 62
FAQs on Factors of 186
1.What are the factors of 186?
2.Mention the prime factors of 186.
3.Is 186 a multiple of 62?
4.Mention the factor pairs of 186?
5.What is the square of 186?
Important Glossaries for Factors of 186
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 186 are 1, 2, 3, 6, 31, 62, 93, and 186.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 31 are prime factors of 186.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 186 are (1, 186), (2, 93), etc.
- Prime factorization: Breaking down a number into the multiplication of its prime factors. For example, the prime factorization of 186 is 2 × 3 × 31.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 186 is a multiple of 62.
Explore More numbers
Previous to Factors of 186
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
