124 LearnersLast updated on May 26th, 2025
Factors of 381
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 381, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 381?
The numbers that divide 381 evenly are known as factors of 381. A factor of 381 is a number that divides the number without remainder.
The factors of 381 are 1, 3, 127, and 381.
Negative factors of 381: -1, -3, -127, and -381.
Prime factors of 381: 3 and 127.
Prime factorization of 381: 3 × 127.
The sum of factors of 381: 1 + 3 + 127 + 381 = 512
How to Find Factors of 381?
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 381. Identifying the numbers which are multiplied to get the number 381 is the multiplication method.
Step 1: Multiply 381 by 1, 381 × 1 = 381.
Step 2: Check for other numbers that give 381 after multiplying
3 × 127 = 381
Therefore, the positive factor pairs of 381 are: (1, 381) and (3, 127). All these factor pairs result in 381. 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 381 by 1, 381 ÷ 1 = 381.
Step 2: Continue dividing 381 by the numbers until the remainder becomes 0.
- 381 ÷ 1 = 381
- 381 ÷ 3 = 127
Therefore, the factors of 381 are: 1, 3, 127, 381.
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 381 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
381 ÷ 3 = 127
127 is a prime number, so we stop here. The prime factors of 381 are 3 and 127.
The prime factorization of 381 is: 3 × 127.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 381 is divided by 3 to get 127.
Step 2: Since 127 is a prime number, it cannot be divided further. So, the prime factorization of 381 is: 3 × 127.
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 381: (1, 381) and (3, 127).
Negative factor pairs of 381: (-1, -381) and (-3, -127).
Common Mistakes and How to Avoid Them in Factors of 381
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 381, 1 and 381 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 381 consist of -1, -3, -127, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 381/1.5 ≈ 254, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 381 are prime numbers. For example, 3 and 127 are the prime factors of 381, but it has other factors like 1, 381.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 381 as 3 × 127 and missing all the key factors.
Factors of 381 Examples
Problem 1
There are 3 teams and 381 participants. How will they divide them equally?
They will get 127 participants each.
Explanation
To divide the participants equally, we need to divide the total participants by the number of teams.
381/3 = 127
Problem 2
A banner is rectangular, the length of the banner is 3 meters and the total area is 381 square meters. Find the width.
127 meters.
Explanation
To find the width of the banner, we use the formula,
Area = length × width
381 = 3 × width
To find the value of width, we need to shift 3 to the left side.
381/3 = width
Width = 127.
Problem 3
There are 127 boxes and 381 items. How many items will be in each box?
Each box will have 3 items.
Explanation
To find the items in each box, divide the total items by the boxes.
381/127 = 3
Problem 4
In a tournament, there are 381 players and 3 divisions. How many players are there in each division?
There are 127 players in each division.
Explanation
Dividing the players by the total divisions, we will get the number of players in each division.
381/3 = 127
Problem 5
381 chairs need to be arranged in 3 rows. How many chairs will go in each row?
Each of the rows has 127 chairs.
Explanation
Divide total chairs by rows.
381/3 = 127
FAQs on Factors of 381
1.What are the factors of 381?
2.Mention the prime factors of 381.
3.Is 381 a multiple of 3?
4.Mention the factor pairs of 381?
5.What is the square of 381?
6.How can children in United States use numbers in everyday life to understand Factors of 381?
7.What are some fun ways kids in United States can practice Factors of 381 with numbers?
8.What role do numbers and Factors of 381 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 381 skills?
Important Glossaries for Factor of 381
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 381 are 1, 3, 127, and 381.
- Prime factors: The factors which are prime numbers. For example, 3 and 127 are prime factors of 381.
- 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 381 are (1, 381) and (3, 127).
- Prime factorization: The expression of a number as a product of its prime factors. For 381, it is 3 × 127.
- Negative factors: These are negative numbers that divide the original number completely. For example, the negative factors of 381 are -1, -3, -127, and -381.
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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.
