125 LearnersLast updated on May 26th, 2025
Factors of 25
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 25, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 25?
The numbers that divide 25 evenly are known as factors of 25.
A factor of 25 is a number that divides the number without remainder.
The factors of 25 are 1, 5, and 25.
Negative factors of 25: -1, -5, and -25.
Prime factors of 25: 5.
Prime factorization of 25: 5².
The sum of factors of 25: 1 + 5 + 25 = 31
How to Find Factors of 25?
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 25. Identifying the numbers which are multiplied to get the number 25 is the multiplication method.
Step 1: Multiply 25 by 1, 25 × 1 = 25.
Step 2: Check for other numbers that give 25 after multiplying 5 × 5 = 25.
Therefore, the positive factor pairs of 25 are: (1, 25) and (5, 5). 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 25 by 1, 25 ÷ 1 = 25.
Step 2: Continue dividing 25 by the numbers until the remainder becomes 0.
25 ÷ 1 = 25
25 ÷ 5 = 5
Therefore, the factors of 25 are: 1, 5, and 25.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers.
We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
- Using Prime Factorization
Using Prime Factorization: In this process, prime factors of 25 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factor of 25 is 5.
The prime factorization of 25 is: 5².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 25 is divided by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 25 is: 5².
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 25: (1, 25) and (5, 5).
Negative factor pairs of 25: (-1, -25) and (-5, -5).
Common Mistakes and How to Avoid Them in Factors of 25
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 25, 1 and 25 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 25 consist of -1, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 2.5 is a factor because 25/2.5 = 10, but 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 25 are prime numbers.
For example, 5 is the prime factor of 25, but it has other factors like 1 and 25.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not recognizing 25 as 5² and missing all the key factors.
Factors of 25 Examples
Problem 1
There is a garden with 25 flowers, and you want to plant them in rows with an equal number of flowers in each row. If you want each row to have the same number of flowers, how many different ways can you arrange them?
You can arrange the flowers in 3 different ways:
1 row of 25 flowers, 5 rows of 5 flowers, or 25 rows of 1 flower each.
Explanation
To find the number of different ways to arrange the flowers, we need to consider the factor pairs of 25.
The factor pairs are (1, 25) and (5, 5).
Problem 2
You have a rope that is 25 meters long. You want to cut it into equal pieces with no rope left over. What are the different lengths you can cut the rope into?
You can cut the rope into lengths of 1 meter, 5 meters, or 25 meters.
Explanation
To find the different lengths, we use the factors of 25.
The factors are 1, 5, and 25.
Problem 3
A teacher has 25 pencils and wants to distribute them equally among 5 students. How many pencils will each student receive?
Each student will receive 5 pencils.
Explanation
To distribute the pencils equally, divide the total pencils by the number of students.
25/5 = 5
Problem 4
There are 25 chairs that need to be arranged in rows. If each row must have the same number of chairs and you want at least 5 rows, how many chairs will be in each row?
There will be 5 chairs in each row.
Explanation
To find the number of chairs per row, divide the total number of chairs by the number of rows.
25/5 = 5
Problem 5
You want to divide 25 apples equally among your family of 5 people. How many apples does each person get?
Each person gets 5 apples.
Explanation
To divide the apples equally, divide the total apples by the number of people.
25/5 = 5
FAQs on Factors of 25
1.What are the factors of 25?
2.Mention the prime factorization of 25.
3.Is 25 a multiple of 5?
4.Mention the factor pairs of 25?
5.What is the square of 25?
6.How can children in Qatar use numbers in everyday life to understand Factors of 25?
7.What are some fun ways kids in Qatar can practice Factors of 25 with numbers?
8.What role do numbers and Factors of 25 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 25 skills?
Important Glossaries for Factors of 25
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 25 are 1, 5, and 25.
- Prime factors: The factors which are prime numbers. For example, 5 is a prime factor of 25. 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 25 are (1, 25) and (5, 5).
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 25 is 5².
- Multiplication method: A method to determine factors by identifying pairs of numbers that can be multiplied to produce the original number. For example, using multiplication to find factor pairs of 25.
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About BrightChamps in Qatar
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.
