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102 LearnersLast updated on September 9, 2025
GCF of 25 and 36
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 25 and 36.
What is the GCF of 25 and 36?
The greatest common factor of 25 and 36 is 1. The largest divisor of two or more numbers is called the GCF of the numbers.
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 36?
To find the GCF of 25 and 36, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 25 and 36 by Using Listing of factors
Steps to find the GCF of 25 and 36 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 25 = 1, 5, 25. Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 2: Now, identify the common factors of them Common factors of 25 and 36: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 25 and 36 is 1.
GCF of 25 and 36 Using Prime Factorization
To find the GCF of 25 and 36 using the 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 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1. The Greatest Common Factor of 25 and 36 is 1.
GCF of 25 and 36 Using Division Method or Euclidean Algorithm Method
Find the GCF of 25 and 36 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 36 by 25 36 ÷ 25 = 1 (quotient), The remainder is calculated as 36 − (25×1) = 11 The remainder is 11, not zero, so continue the process
Step 2: Now divide the previous divisor (25) by the previous remainder (11) 25 ÷ 11 = 2 (quotient), remainder = 25 − (11×2) = 3
Step 3: Now divide the previous divisor (11) by the previous remainder (3) 11 ÷ 3 = 3 (quotient), remainder = 11 − (3×3) = 2
Step 4: Now divide the previous divisor (3) by the previous remainder (2) 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 1
Step 5: Finally, divide the previous divisor (2) by the previous remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 25 and 36 is 1.
Common Mistakes and How to Avoid Them in GCF of 25 and 36
Finding the GCF of 25 and 36 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, even if it is 1.
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 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 will always be greater than 1. But it's not true; the GCF can be 1 as well, especially for co-prime numbers.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 25 and 36 Examples
Problem 1
A gardener has 25 tulips and 36 roses. She wants to plant them in equal-sized groups, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 25 and 36 GCF of 25 and 36 is 1.
So, each group will have 1 flower.
Explanation
As the GCF of 25 and 36 is 1, the gardener can plant them in groups of 1 flower each.
Problem 2
A school has 25 red markers and 36 blue markers. They want to place them in rows with the same number of markers in each row, using the largest possible number of markers per row. How many markers will be in each row?
GCF of 25 and 36 is 1. So each row will have 1 marker.
Explanation
There are 25 red and 36 blue markers.
To find the total number of markers in each row, we should find the GCF of 25 and 36.
Each row will have 1 marker.
Problem 3
A tailor has 25 meters of silk ribbon and 36 meters of cotton ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 25 and 36 The GCF of 25 and 36 is 1. The ribbon is 1 meter long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 25 and 36, which is 1.
The length of each piece of the ribbon will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 25 cm long and the other 36 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 25 and 36 is 1.
The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 25 cm and 36 cm respectively, we have to find the GCF of 25 and 36, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 25 and ‘b’ is 1, and the LCM is 900. Find ‘b’.
The value of ‘b’ is 36.
Explanation
GCF x LCM = product of the numbers
1 × 900
= 25 × b 900
= 25b b
= 900 ÷ 25 = 36
FAQs on the Greatest Common Factor of 25 and 36
1.What is the LCM of 25 and 36?
2.Is 25 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 36?
5.Are 25 and 36 prime numbers?
Important Glossaries for GCF of 25 and 36
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 4, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 7 is 35.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 15 and 25 will be 5, as it is their largest common factor that divides the numbers completely.
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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.
