121 LearnersLast updated on May 26th, 2025
Factors of 25000
Factors are the numbers that divide a 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 25000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 25000?
The numbers that divide 25000 evenly are known as factors of 25000.
A factor of 25000 is a number that divides the number without remainder.
The factors of 25000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 500, 625, 1250, 2500, 5000, 12500, and 25000.
Negative factors of 25000: -1, -2, -4, -5, -8, -10, -16, -20, -25, -40, -50, -80, -100, -125, -200, -250, -500, -625, -1250, -2500, -5000, -12500, and -25000.
Prime factors of 25000: 2 and 5.
Prime factorization of 25000: 24 × 56.
The sum of factors of 25000: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 40 + 50 + 80 + 100 + 125 + 200 + 250 + 500 + 625 + 1250 + 2500 + 5000 + 12500 + 25000 = 65535
How to Find Factors of 25000?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 25000. Identifying the numbers which are multiplied to get the number 25000 is the multiplication method.
Step 1: Multiply 25000 by 1, 25000 × 1 = 25000.
Step 2: Check for other numbers that give 25000 after multiplying
2 × 12500 = 25000
4 × 6250 = 25000
5 × 5000 = 25000
8 × 3125 = 25000
10 × 2500 = 25000
25 × 1000 = 25000
50 × 500 = 25000
100 × 250 = 25000
125 × 200 = 25000
250 × 100 = 25000
500 × 50 = 25000
625 × 40 = 25000
1250 × 20 = 25000
2500 × 10 = 25000
5000 × 5 = 25000
12500 × 2 = 25000
Therefore, the positive factor pairs of 25000 are: (1, 25000), (2, 12500), (4, 6250), (5, 5000), (8, 3125), (10, 2500), (25, 1000), (50, 500), (100, 250), (125, 200), (250, 100), (500, 50), (625, 40), (1250, 20), (2500, 10), (5000, 5), (12500, 2). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following the simple division method -
Step 1: Divide 25000 by 1, 25000 ÷ 1 = 25000.
Step 2: Continue dividing 25000 by the numbers until the remainder becomes 0.
25000 ÷ 1 = 25000
25000 ÷ 2 = 12500
25000 ÷ 4 = 6250
25000 ÷ 5 = 5000
25000 ÷ 8 = 3125
25000 ÷ 10 = 2500
25000 ÷ 25 = 1000
25000 ÷ 50 = 500
25000 ÷ 100 = 250
25000 ÷ 125 = 200
25000 ÷ 250 = 100
25000 ÷ 500 = 50
25000 ÷ 625 = 40
25000 ÷ 1250 = 20
25000 ÷ 2500 = 10
Therefore, the factors of 25000 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 500, 625, 1250, 2500, 5000, 12500, 25000.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 25000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
25000 ÷ 2 = 12500
12500 ÷ 2 = 6250
6250 ÷ 2 = 3125
3125 ÷ 5 = 625
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 25000 are 2 and 5.
The prime factorization of 25000 is: 24 × 56.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 25000 is divided by 2 to get 12500.
Step 2: Now divide 12500 by 2 to get 6250.
Step 3: Then divide 6250 by 2 to get 3125.
Step 4: Divide 3125 by 5 to get 625.
Step 5: Divide 625 by 5 to get 125.
Step 6: Divide 125 by 5 to get 25.
Step 7: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 25000 is: 24 × 56.
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 25000: (1, 25000), (2, 12500), (4, 6250), (5, 5000), (8, 3125), (10, 2500), (25, 1000), (50, 500), (100, 250), (125, 200), (250, 100), (500, 50), (625, 40), (1250, 20), (2500, 10), (5000, 5), (12500, 2).
Negative factor pairs of 25000: (-1, -25000), (-2, -12500), (-4, -6250), (-5, -5000), (-8, -3125), (-10, -2500), (-25, -1000), (-50, -500), (-100, -250), (-125, -200), (-250, -100), (-500, -50), (-625, -40), (-1250, -20), (-2500, -10), (-5000, -5), (-12500, -2).
Common Mistakes and How to Avoid Them in Factors of 25000
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 25000, 1 and 25000 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 25000 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor because 25000/1.5 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 25000 are prime numbers. For example, 2 and 5 are the prime factors of 25000, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 25000 as 2^4 × 5^6 and missing all the key factors.
Factors of 25000 Examples
Problem 1
A carpenter has 25000 nails and 250 boxes. How many nails will go in each box?
Each box will have 100 nails.
Explanation
To determine the number of nails in each box, divide the total nails by the number of boxes.
25000/250 = 100
Problem 2
A rectangular garden has an area of 25000 square meters, and its width is 125 meters. What is its length?
200 meters.
Explanation
To find the length of the garden, use the formula,
Area = length × width
25000 = length × 125
To find the value of length, divide the area by the width.
25000/125 = length
Length = 200.
Problem 3
There are 5000 apples that need to be divided equally among 25 baskets. How many apples will each basket contain?
Each basket will contain 200 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
5000/25 = 200
Problem 4
A farmer has a field that is 500 meters long and 50 meters wide. Calculate the area of the field.
The area of the field is 25000 square meters.
Explanation
To find the area of the field, use the formula,
Area = length × width
Area = 500 × 50 = 25000 square meters
Problem 5
25000 seeds need to be packed into 125 bags. How many seeds will go in each bag?
Each bag will have 200 seeds.
Explanation
Divide the total seeds by the number of bags.
25000/125 = 200
FAQs on Factors of 25000
1.What are the factors of 25000?
2.Mention the prime factors of 25000.
3.Is 25000 a multiple of 50?
4.Mention the factor pairs of 25000?
5.What is the square of 250?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 25000?
7.What are some fun ways kids in Vietnam can practice Factors of 25000 with numbers?
8.What role do numbers and Factors of 25000 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 25000 skills?
Important Glossaries for Factors of 25000
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 25000 are 1, 2, 4, 5, 8, etc.
- Prime factors: Factors which are prime numbers. For example, 2 and 5 are prime factors of 25000.
- 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 25000 are (1, 25000), (2, 12500), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 25000 is 24 × 56.
- Multiples: Numbers that can be divided by another number without a remainder. For example, 25000 is a multiple of 50.
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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.
