106 LearnersLast updated on May 26th, 2025
Factors of 111
Factors are the numbers that divide any given number evenly without a 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 111, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 111?
The numbers that divide 111 evenly are known as factors of 111. A factor of 111 is a number that divides the number without a remainder. The factors of 111 are 1, 3, 37, and 111
Negative factors of 111: -1, -3, -37, and -111.
Prime factors of 111: 3 and 37.
Prime factorization of 111: 3 × 37.
The sum of factors of 111: 1 + 3 + 37 + 111 = 152
How to Find Factors of 111?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 111. Identifying the numbers which are multiplied to get the number 111 is the multiplication method.
Step 1: Multiply 111 by 1, 111 × 1 = 111.
Step 2: Check for other numbers that give 111 after multiplying 3 × 37 = 111
Therefore, the positive factor pairs of 111 are: (1, 111) and (3, 37). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 111 by 1, 111 ÷ 1 = 111.
Step 2: Continue dividing 111 by the numbers until the remainder becomes 0.
111 ÷ 1 = 111
111 ÷ 3 = 37
Therefore, the factors of 111 are: 1, 3, 37, and 111.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. 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 111 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
111 ÷ 3 = 37
37 ÷ 37 = 1
The prime factors of 111 are 3 and 37. The prime factorization of 111 is: 3 × 37.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 111 is divided by 3 to get 37.
Step 2: Now divide 37 by 37 to get 1. Here, 37 is a prime number, that cannot be divided anymore. So, the prime factorization of 111 is: 3 × 37.
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 111: (1, 111) and (3, 37).
- Negative factor pairs of 111: (-1, -111) and (-3, -37).
Common Mistakes and How to Avoid Them in Factors of 111
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 111, 1 and 111 are also factors.
Factors of 111 Examples
Problem 1
There are 3 teams and 111 participants. How will they divide them equally?
They will have 37 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
111/3 = 37
Problem 2
A farmer has a rectangular plot with a length of 37 meters and a total area of 111 square meters. Find the width?
3 meters.
Explanation
To find the width of the plot, we use the formula,
Area = length × width
111 = 37 × width
To find the value of width, we need to shift 37 to the left side.
111/37 = width
Width = 3.
Problem 3
There are 111 candies and 37 bags. How many candies will be in each bag?
Each bag will have 3 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
111/37 = 3
Problem 4
In a class, there are 111 students, and they need to form 3 groups. How many students are there in each group?
There are 37 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
111/3 = 37
Problem 5
111 books need to be arranged on 37 shelves. How many books will go on each shelf?
Each shelf has 3 books.
Explanation
Divide total books by shelves.
111/37 = 3
FAQs on Factors of 111
1.What are the factors of 111?
2.Mention the prime factors of 111.
3.Is 111 a multiple of 3?
4.Mention the factor pairs of 111?
5.What is the square of 111?
Important Glossaries for Factors of 111
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 111 are 1, 3, 37, and 111.
- Prime factors: The factors which are prime numbers. For example, 3 and 37 are prime factors of 111.
- 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 111 are (1, 111) and (3, 37).
- Multiplication method: A method to find factors by identifying pairs of numbers multiplied to get the original number.
- Division method: A method to find factors by dividing the number by whole numbers to see which divisions result in whole numbers without a remainder.
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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.
