126 LearnersLast updated on May 26th, 2025
Factors of 361
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 361, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 361?
The numbers that divide 361 evenly are known as factors of 361.
A factor of 361 is a number that divides the number without remainder.
The factors of 361 are 1, 19, and 361.
Negative factors of 361: -1, -19, and -361.
Prime factors of 361: 19.
Prime factorization of 361: 19 × 19.
The sum of factors of 361: 1 + 19 + 361 = 381
How to Find Factors of 361?
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 361. Identifying the numbers which are multiplied to get the number 361 is the multiplication method.
Step 1: Multiply 361 by 1, 361 × 1 = 361.
Step 2: Check for other numbers that give 361 after multiplying 19 × 19 = 361
Therefore, the positive factor pairs of 361 are: (1, 361) and (19, 19).
All these factor pairs result in 361.
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 simple division method
Step 1: Divide 361 by 1, 361 ÷ 1 = 361.
Step 2: Continue dividing 361 by the numbers until the remainder becomes 0.
361 ÷ 1 = 361
361 ÷ 19 = 19
Therefore, the factors of 361 are: 1, 19, and 361.
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 361 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
361 ÷ 19 = 19
19 ÷ 19 = 1
The prime factor of 361 is 19.
The prime factorization of 361 is: 19 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 361 is divided by 19 to get 19.
Step 2: Now divide 19 by 19 to get 1. Here, 19 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 361 is: 19 × 19.
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 361: (1, 361) and (19, 19).
Negative factor pairs of 361: (-1, -361) and (-19, -19).
Common Mistakes and How to Avoid Them in Factors of 361
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 361, 1 and 361 are also factors.
Mistake 2
Missing Negative Factors
We often tend to mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 361 include -1, -19, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 361/1.5 = 240.666, 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 361 are prime numbers.
For example, 19 is a prime factor of 361, but it also has other factors like 1 and 361.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 361 as 19 × 19 and missing all the key factors.
Factors of 361 Examples
Problem 1
A cake has 361 pieces and needs to be shared equally among 19 guests. How many pieces will each guest receive?
Each guest will receive 19 pieces.
Explanation
To divide the cake equally, we need to divide the total pieces by the number of guests.
361/19 = 19
Problem 2
A square garden has an area of 361 square meters. What is the length of each side of the garden?
19 meters.
Explanation
To find the length of each side of the square garden, take the square root of the area.
√361 = 19
Problem 3
A school has 361 students, and the students are to form groups with an equal number of students. If each group has 19 students, how many groups can be formed?
19 groups can be formed.
Explanation
To find the number of groups, divide the total number of students by the number of students per group.
361/19 = 19
Problem 4
There are 361 apples, and they need to be packed into boxes containing 19 apples each. How many boxes are needed?
19 boxes are needed.
Explanation
Divide the total number of apples by the number of apples per box.
361/19 = 19
Problem 5
A library has 361 books, and each shelf can hold 19 books. How many shelves are required to store all the books?
19 shelves are required.
Explanation
Divide the total number of books by the number of books per shelf.
361/19 = 19
FAQs on Factors of 361
1.What are the factors of 361?
2.Mention the prime factors of 361.
3.Is 361 a multiple of 19?
4.Mention the factor pairs of 361?
5.What is the square of 19?
6.How can children in India use numbers in everyday life to understand Factors of 361?
7.What are some fun ways kids in India can practice Factors of 361 with numbers?
8.What role do numbers and Factors of 361 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 361 skills?
Important Glossaries for Factors of 361
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 361 are 1, 19, and 361.
- Prime factors: The factors which are prime numbers. For example, 19 is a prime factor of 361.
- 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 361 are (1, 361) and (19, 19).
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 361 is 19 × 19.
- Multiplication method: A way to find factors by identifying pairs of numbers that multiply to give the original number. For example, finding factor pairs of 361 through multiplication results in (1, 361) and (19, 19).
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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.
