102 LearnersLast updated on May 26th, 2025
Factors of 5625
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 5625, how they are used in real life, and tips to learn them quickly.
What are the Factors of 5625?
The numbers that divide 5625 evenly are known as factors of 5625.
A factor of 5625 is a number that divides the number without remainder.
The factors of 5625 are 1, 3, 5, 15, 25, 75, 225, 375, 1125, 1875, and 5625.
Negative factors of 5625: -1, -3, -5, -15, -25, -75, -225, -375, -1125, -1875, and -5625.
Prime factors of 5625: 3 and 5.
Prime factorization of 5625: 3² × 5⁴.
The sum of factors of 5625: 1 + 3 + 5 + 15 + 25 + 75 + 225 + 375 + 1125 + 1875 + 5625 = 9354
How to Find Factors of 5625?
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 5625. Identifying the numbers which are multiplied to get the number 5625 is the multiplication method.
Step 1: Multiply 5625 by 1, 5625 × 1 = 5625.
Step 2: Check for other numbers that give 5625 after multiplying
3 × 1875 = 5625
5 × 1125 = 5625
15 × 375 = 5625
25 × 225 = 5625
75 × 75 = 5625
Therefore, the positive factor pairs of 5625 are: (1, 5625), (3, 1875), (5, 1125), (15, 375), (25, 225), (75, 75).
All these factor pairs result in 5625.
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 5625 by 1, 5625 ÷ 1 = 5625.
Step 2: Continue dividing 5625 by the numbers until the remainder becomes 0.
5625 ÷ 1 = 5625
5625 ÷ 3 = 1875
5625 ÷ 5 = 1125
5625 ÷ 15 = 375
5625 ÷ 25 = 225
5625 ÷ 75 = 75
Therefore, the factors of 5625 are: 1, 3, 5, 15, 25, 75, 225, 375, 1125, 1875, 5625.
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 5625 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5625 ÷ 3 = 1875
1875 ÷ 3 = 625
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 5625 are 3 and 5.
The prime factorization of 5625 is: 3² × 5⁴.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 5625 is divided by 3 to get 1875.
Step 2: Now divide 1875 by 3 to get 625.
Step 3: Then divide 625 by 5 to get 125.
Step 4: Divide 125 by 5 to get 25.
Step 5: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5625 is: 3² × 5⁴.
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 5625: (1, 5625), (3, 1875), (5, 1125), (15, 375), (25, 225), and (75, 75).
Negative factor pairs of 5625: (-1, -5625), (-3, -1875), (-5, -1125), (-15, -375), (-25, -225), and (-75, -75).
Common Mistakes and How to Avoid Them in Factors of 5625
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 5625, 1 and 5625 are also factors.
Factors of 5625 Examples
Problem 1
A group of 15 people wants to share 5625 candies equally. How many candies will each person get?
Each person will get 375 candies.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
5625/15 = 375
Problem 2
A square garden has an area of 5625 square meters. What is the length of one side of the garden?
75 meters.
Explanation
To find the length of one side of the garden, we take the square root of the area.
√5625 = 75
Problem 3
There are 25 classrooms and 5625 pencils. How many pencils will be in each classroom?
Each classroom will have 225 pencils.
Explanation
To find the pencils in each classroom, divide the total pencils by the number of classrooms.
5625/25 = 225
Problem 4
In a conference, there are 75 tables, and 5625 chairs. How many chairs are there at each table?
There are 75 chairs at each table.
Explanation
Dividing the chairs by the total tables, we will get the number of chairs at each table.
5625/75 = 75
Problem 5
5625 apples need to be packed into 5 crates. How many apples will go in each crate?
Each of the crates has 1125 apples.
Explanation
Divide total apples by crates.
5625/5 = 1125
FAQs on Factors of 5625
1.What are the factors of 5625?
2.Mention the prime factors of 5625.
3.Is 5625 a multiple of 25?
4.Mention the factor pairs of 5625?
5.What is the square root of 5625?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 5625?
7.What are some fun ways kids in Vietnam can practice Factors of 5625 with numbers?
8.What role do numbers and Factors of 5625 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 5625 skills?
Important Glossaries for Factor of 5625
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5625 are 1, 3, 5, 15, 25, 75, 225, 375, 1125, 1875, and 5625.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of 5625.
- 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 5625 are (1, 5625), (3, 1875), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 5625 is 3² × 5⁴.
- Square root: A value that, when multiplied by itself, gives the original number. For example, the square root of 5625 is 75.
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About BrightChamps in Vietnam
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.
