101 LearnersLast updated on May 26th, 2025
Factors of 2401
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 2401, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2401?
The numbers that divide 2401 evenly are known as factors of 2401.
A factor of 2401 is a number that divides the number without remainder.
The factors of 2401 are 1, 7, 49, 343, and 2401.
Negative factors of 2401: -1, -7, -49, -343, and -2401.
Prime factor of 2401: 7.
Prime factorization of 2401: 7^4.
The sum of factors of 2401: 1 + 7 + 49 + 343 + 2401 = 2801
How to Find Factors of 2401?
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 2401. Identifying the numbers which are multiplied to get the number 2401 is the multiplication method.
Step 1: Multiply 2401 by 1, 2401 × 1 = 2401.
Step 2: Check for other numbers that give 2401 after multiplying
7 × 343 = 2401
49 × 49 = 2401
Therefore, the positive factor pairs of 2401 are: (1, 2401), (7, 343), (49, 49).
All these factor pairs result in 2401.
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 2401 by 1, 2401 ÷ 1 = 2401.
Step 2: Continue dividing 2401 by the numbers until the remainder becomes 0.
2401 ÷ 1 = 2401
2401 ÷ 7 = 343
2401 ÷ 49 = 49
Therefore, the factors of 2401 are: 1, 7, 49, 343, 2401.
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 2401 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2401 ÷ 7 = 343
343 ÷ 7 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
The prime factor of 2401 is 7.
The prime factorization of 2401 is: 7^4.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2401 is divided by 7 to get 343.
Step 2: Now divide 343 by 7 to get 49.
Step 3: Then divide 49 by 7 to get 7.
Here, 7 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 2401 is: 7^4.
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 2401: (1, 2401), (7, 343), (49, 49).
Negative factor pairs of 2401: (-1, -2401), (-7, -343), (-49, -49).
Common Mistakes and How to Avoid Them in Factors of 2401
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 2401, 1 and 2401 is also a factor.
Factors of 2401 Examples
Problem 1
There are 343 apples and 2401 oranges. How many apples will each person get if the fruit is divided equally among 7 people?
Each person will get 49 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of people.
343/7 = 49
Problem 2
A square garden has an area of 2401 square meters. What is the length of each side of the garden?
49 meters.
Explanation
The area of a square is given by side × side. So, the side length is the square root of the area.
√2401 = 49
Problem 3
A chocolate factory packs chocolates in boxes containing 49 chocolates each. If the factory produces 2401 chocolates, how many boxes are needed?
The factory needs 49 boxes.
Explanation
To find the number of boxes needed, divide the total chocolates by the chocolates per box.
2401/49 = 49
Problem 4
In a stadium, there are 2401 seats arranged in rows of 49 seats each. How many rows are there?
There are 49 rows.
Explanation
Dividing the total seats by the seats per row will give the number of rows.
2401/49 = 49
Problem 5
A baker has 2401 cookies and wants to pack them into boxes containing 7 cookies each. How many boxes will the baker need?
The baker will need 343 boxes.
Explanation
Divide the total cookies by cookies per box.
2401/7 = 343
FAQs on Factors of 2401
1.What are the factors of 2401?
2.Mention the prime factor of 2401.
3.Is 2401 a multiple of 49?
4.Mention the factor pairs of 2401?
5.What is the cube of 7?
6.How can children in Canada use numbers in everyday life to understand Factors of 2401?
7.What are some fun ways kids in Canada can practice Factors of 2401 with numbers?
8.What role do numbers and Factors of 2401 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 2401 skills?
Important Glossaries for Factor of 2401
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2401 are 1, 7, 49, 343, and 2401.
- Prime factor: The factor which is a prime number. For example, 7 is the prime factor of 2401.
- 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 2401 are (1, 2401), (7, 343), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 2401 is 7^4.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number. For example, 7 × 343 = 2401.
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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
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