102 LearnersLast updated on August 5th, 2025
GCF of 25 and 4
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 25 and 4.
What is the GCF of 25 and 4?
The greatest common factor of 25 and 4 is 1. The largest divisor of two or more numbers is called the GCF of the number.
If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 25 and 4?
To find the GCF of 25 and 4, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 25 and 4 by Using Listing of Factors
Steps to find the GCF of 25 and 4 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 25 = 1, 5, 25. Factors of 4 = 1, 2, 4.
Step 2: Now, identify the common factors of them
Common factors of 25 and 4: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 25 and 4 is 1.
GCF of 25 and 4 Using Prime Factorization
To find the GCF of 25 and 4 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 25: 25 = 5 x 5 = 5²
Prime Factors of 4: 4 = 2 x 2 = 2²
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: The GCF of 25 and 4 is 1.
GCF of 25 and 4 Using Division Method or Euclidean Algorithm Method
Find the GCF of 25 and 4 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 25 by 4 25 ÷ 4 = 6 (quotient),
The remainder is calculated as 25 − (4×6) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (4) by the previous remainder (1)
Divide 4 by 1 4 ÷ 1 = 4 (quotient), remainder = 4 − (1×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 25 and 4 is 1.
Common Mistakes and How to Avoid Them in GCF of 25 and 4
Finding the GCF of 25 and 4 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 25, students may mention 10, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always greater than 1
Students may assume that the GCF of two numbers is always greater than 1. But it's not true; the GCF can also be 1 if the numbers are co-prime.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 25 and 4 Examples
Problem 1
A gardener has 25 roses and 4 tulips. She wants to plant them in rows with the greatest number of flowers in each row. How many flowers will be in each row?
We should find the GCF of 25 and 4 The GCF of 25 and 4 is 1. There will be 1 flower in each row.
Explanation
As the GCF of 25 and 4 is 1, the gardener can only plant 1 flower in each row, mixing roses and tulips.
Problem 2
A baker has 25 loaves of bread and 4 cakes. He wants to package them into boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
The GCF of 25 and 4 is 1. So each box will have 1 item.
Explanation
There are 25 loaves of bread and 4 cakes.
To find the total number of items in each box, we should find the GCF of 25 and 4.
There will be 1 item in each box.
Problem 3
A jeweler has 25 gold chains and 4 silver rings. She wants to display them in showcases with the same number of items in each showcase, using the largest possible number of items per showcase. How many items will be in each showcase?
For calculating the largest equal number of items, we have to calculate the GCF of 25 and 4 The GCF of 25 and 4 is 1. The showcase will have 1 item.
Explanation
For calculating the largest number of items in each showcase, first we need to calculate the GCF of 25 and 4, which is 1.
Each showcase will have 1 item.
Problem 4
A farmer has two plots of land, one 25 acres and the other 4 acres. She wants to divide them into equal sections with the largest possible area. What should be the area of each section?
The farmer needs the largest section of land The GCF of 25 and 4 is 1. The largest area of each section is 1 acre.
Explanation
To find the largest area of each section of the two plots of land, 25 acres and 4 acres, respectively, we have to find the GCF of 25 and 4, which is 1 acre.
The largest area of each section is 1 acre.
Problem 5
If the GCF of 25 and 'b' is 1, and the LCM is 100, find 'b'.
The value of 'b' is 4.
Explanation
GCF x LCM = product of the numbers
1 × 100 = 25 × b
100 = 25b
b = 100 ÷ 25 = 4
FAQs on the Greatest Common Factor of 25 and 4
1.What is the LCM of 25 and 4?
2.Is 25 divisible by 5?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 4?
5.Are 25 and 4 prime numbers?
6.How can children in Philippines use numbers in everyday life to understand GCF of 25 and 4?
7.What are some fun ways kids in Philippines can practice GCF of 25 and 4 with numbers?
8.What role do numbers and GCF of 25 and 4 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 25 and 4 skills?
Important Glossaries for GCF of 25 and 4
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Co-prime: Two numbers are co-prime if their only common factor is 1. For example, 9 and 4 are co-prime numbers.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 7 is 35.
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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.
