116 LearnersLast updated on May 26th, 2025
Factors of 7225
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 7225, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 7225?
The numbers that divide 7225 evenly are known as factors of 7225.
A factor of 7225 is a number that divides the number without remainder.
The factors of 7225 are 1, 5, 25, 289, 1445, and 7225.
Negative factors of 7225: -1, -5, -25, -289, -1445, and -7225.
Prime factors of 7225: 5 and 17.
Prime factorization of 7225: 52 × 172.
The sum of factors of 7225: 1 + 5 + 25 + 289 + 1445 + 7225 = 8990
How to Find Factors of 7225?
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 7225. Identifying the numbers which are multiplied to get the number 7225 is the multiplication method.
Step 1: Multiply 7225 by 1, 7225 × 1 = 7225.
Step 2: Check for other numbers that give 7225 after multiplying:
5 × 1445 = 7225
25 × 289 = 7225
Therefore, the positive factor pairs of 7225 are: (1, 7225), (5, 1445), (25, 289).
All these factor pairs result in 7225.
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 the simple division method:
Step 1: Divide 7225 by 1, 7225 ÷ 1 = 7225.
Step 2: Continue dividing 7225 by the numbers until the remainder becomes 0.
7225 ÷ 1 = 7225
7225 ÷ 5 = 1445
7225 ÷ 25 = 289
Therefore, the factors of 7225 are: 1, 5, 25, 289, 1445, 7225.
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 7225 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
7225 ÷ 5 = 1445
1445 ÷ 5 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
The prime factors of 7225 are 5 and 17.
The prime factorization of 7225 is: 52 × 172.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 7225 is divided by 5 to get 1445.
Step 2: Now divide 1445 by 5 to get 289.
Step 3: Then divide 289 by 17 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 7225 is: 52 × 172.
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 7225: (1, 7225), (5, 1445), (25, 289).
Negative factor pairs of 7225: (-1, -7225), (-5, -1445), (-25, -289).
Common Mistakes and How to Avoid Them in Factors of 7225
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 word. Always remember to include 1 and the number itself.
For example, in factors of 7225, 1 and 7225 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 7225 consist of -1, -5, -25, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 7225/1.5 = 4816.6667, 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 7225 are prime numbers.
For example, 5 and 17 are the prime factors of 7225, but it has other factors like 25, 289.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 7225 as 52 × 172 and missing all the key factors.
Factors of 7225 Examples
Problem 1
There are 5 teachers and 7225 pens. How will they divide it equally?
They will get 1445 pens each.
Explanation
To divide the pens equally, we need to divide the total pens with the number of teachers.
7225/5 = 1445
Problem 2
A rectangular garden has a length of 25 meters and a total area of 7225 square meters. Find the width.
289 meters.
Explanation
To find the width of the garden, we use the formula:
Area = length × width
7225 = 25 × width
To find the value of width, we need to shift 25 to the left side.
7225/25 = width
Width = 289.
Problem 3
There are 289 students and 7225 notebooks. How many notebooks will each student receive?
Each student will receive 25 notebooks.
Explanation
To find the notebooks each student receives, divide the total notebooks by the number of students.
7225/289 = 25
Problem 4
In a class, there are 25 groups, and 7225 chocolates. How many chocolates are there in each group?
There are 289 chocolates in each group.
Explanation
Dividing the chocolates with the total groups, we will get the number of chocolates in each group.
7225/25 = 289
Problem 5
7225 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 1445 books.
Explanation
Divide total books with shelves.
7225/5 = 1445
FAQs on Factors of 7225
1.What are the factors of 7225?
2.Mention the prime factors of 7225.
3.Is 7225, a multiple of 5?
4.Mention the factor pairs of 7225?
5.What is the square of 7225?
6.How can children in United States use numbers in everyday life to understand Factors of 7225?
7.What are some fun ways kids in United States can practice Factors of 7225 with numbers?
8.What role do numbers and Factors of 7225 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 7225 skills?
Important Glossaries for Factors of 7225
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7225 are 1, 5, 25, 289, 1445, and 7225.
- Prime factors: The factors which are prime numbers. For example, 5 and 17 are prime factors of 7225.
- 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 7225 are (1, 7225), (5, 1445), etc.
- Prime factorization: Breaking down a number into its prime number components. For example, the prime factorization of 7225 is 52 × 172.
- Negative factors: The negative counterparts of the positive factors of a number. For example, the negative factors of 7225 are -1, -5, -25, -289, -1445, and -7225.
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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.
