128 LearnersLast updated on May 26th, 2025
Factors of 3025
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 3025, how they are used in real life, and tips to learn them quickly.
What are the Factors of 3025?
The numbers that divide 3025 evenly are known as factors of 3025.
A factor of 3025 is a number that divides the number without remainder.
The factors of 3025 are 1, 5, 25, 121, 605, and 3025.
Negative factors of 3025: -1, -5, -25, -121, -605, and -3025.
Prime factors of 3025: 5 and 11.
Prime factorization of 3025: 5² × 11².
The sum of factors of 3025: 1 + 5 + 25 + 121 + 605 + 3025 = 3782
How to Find Factors of 3025?
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 3025. Identifying the numbers which are multiplied to get the number 3025 is the multiplication method.
Step 1: Multiply 3025 by 1, 3025 × 1 = 3025.
Step 2: Check for other numbers that give 3025 after multiplying
5 × 605 = 3025
25 × 121 = 3025
Therefore, the positive factor pairs of 3025 are: (1, 3025), (5, 605), (25, 121). All these factor pairs result in 3025. 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 3025 by 1, 3025 ÷ 1 = 3025.
Step 2: Continue dividing 3025 by the numbers until the remainder becomes 0.
3025 ÷ 1 = 3025
3025 ÷ 5 = 605
3025 ÷ 25 = 121
Therefore, the factors of 3025 are: 1, 5, 25, 121, 605, 3025.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 3025 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
3025 ÷ 5 = 605
605 ÷ 5 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factors of 3025 are 5 and 11.
The prime factorization of 3025 is: 5² × 11².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 3025 is divided by 5 to get 605.
Step 2: Now divide 605 by 5 to get 121.
Step 3: Then divide 121 by 11 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3025 is: 5² × 11².
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 3025: (1, 3025), (5, 605), (25, 121).
Negative factor pairs of 3025: (-1, -3025), (-5, -605), (-25, -121).
Common Mistakes and How to Avoid Them in Factors of 3025
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 3025, 1 and 3025 is also a factor.
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 3025 consist of -1, -5, -25, etc.
Mistake 3
Including the Fraction
Children might sometimes add fraction also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 3025/1.5 = 2016.67, 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 3025 are prime numbers.
For example, 5 and 11 are the prime factors of 3025, but it has other factors like 25, 605.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 3025 as 5² × 11² and missing all the key factors.
Factors of 3025 Examples
Problem 1
A theater has 605 seats and is showing a popular movie. If 5 people want to sit in each row, how many rows can be formed?
121 rows can be formed.
Explanation
To find the number of rows, divide the total seats by seats per row.
605/5 = 121
Problem 2
A square photo has an area of 3025 square centimeters. What is the length of one side of the photo?
55 centimeters.
Explanation
To find the length of one side of the square, we take the square root of the area.
√3025 = 55
Problem 3
You have 25 gift boxes and 3025 candies. How many candies can go in each box?
Each box will have 121 candies.
Explanation
To find the candies in each box, divide the total candies by the number of boxes.
3025/25 = 121
Problem 4
A library has 3025 books and wants to place them evenly on 5 shelves. How many books will be on each shelf?
Each of the shelves has 605 books.
Explanation
Divide total books by shelves.
3025/5 = 605
Problem 5
If a garden is 605 square meters and is to be divided into 5 equal sections, what will be the area of each section?
Each section will be 121 square meters.
Explanation
Divide the total area by the number of sections.
605/5 = 121
FAQs on Factors of 3025
1.What are the factors of 3025?
2.Mention the prime factors of 3025.
3.Is 3025 a perfect square?
4.Mention the factor pairs of 3025?
5.What is the square of 55?
6.How can children in United States use numbers in everyday life to understand Factors of 3025?
7.What are some fun ways kids in United States can practice Factors of 3025 with numbers?
8.What role do numbers and Factors of 3025 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 3025 skills?
Important Glossaries for Factor of 3025
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3025 are 1, 5, 25, 121, 605, and 3025.
- Prime factors: The factors which are prime numbers. For example, 5 and 11 are prime factors of 3025.
- 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 3025 are (1, 3025), (5, 605), etc.
- Perfect square: A number that is the square of an integer. For example, 3025 is a perfect square of 55.
- Division method: A method of finding factors by dividing the number by whole numbers until no remainder is left.
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About BrightChamps in United States
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.
