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127 LearnersLast updated on December 11, 2025
GCF of 27 and 125
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 27 and 125.
What is the GCF of 27 and 125?
The greatest common factor of 27 and 125 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 27 and 125?
To find the GCF of 27 and 125, a few methods are described below :-
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 27 and 125 by Using Listing of Factors
Steps to find the GCF of 27 and 125 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 27 = 1, 3, 9, 27. Factors of 125 = 1, 5, 25, 125.
Step 2: Now, identify the common factors of them Common factors of 27 and 125: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 27 and 125 is 1.
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GCF of 27 and 125 Using Prime Factorization
To find the GCF of 27 and 125 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 27: 27 = 3 x 3 x 3 = 3³ Prime Factors of 125: 125 = 5 x 5 x 5 = 5³
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 27 and 125 is 1.
GCF of 27 and 125 Using Division Method or Euclidean Algorithm Method
Find the GCF of 27 and 125 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 125 by 27 125 ÷ 27 = 4 (quotient), The remainder is calculated as 125 − (27×4) = 17 The remainder is 17, not zero, so continue the process.
Step 2: Now divide the previous divisor (27) by the previous remainder (17) Divide 27 by 17 27 ÷ 17 = 1 (quotient), remainder = 27 − (17×1) = 10.
Step 3: Now divide the previous divisor (17) by the previous remainder (10) 17 ÷ 10 = 1 (quotient), remainder = 17 − (10×1) = 7.
Step 4: Now divide the previous divisor (10) by the previous remainder (7) 10 ÷ 7 = 1 (quotient), remainder = 10 − (7×1) = 3.
Step 5: Now divide the previous divisor (7) by the previous remainder (3) 7 ÷ 3 = 2 (quotient), remainder = 7 − (3×2) = 1.
Step 6: Now divide the previous divisor (3) by the previous remainder (1) 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0 The remainder is zero; thus, the divisor is the GCF.
The GCF of 27 and 125 is 1.
Common Mistakes and How to Avoid Them in GCF of 27 and 125
Finding the GCF of 27 and 125 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 27, 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 indicates an 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 will always be greater than 1.
But this is not true for numbers that are co-prime.
To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 27 and 125 Examples
Problem 1
A baker has 27 chocolate cupcakes and 125 vanilla cupcakes. He wants to pack them into boxes with the largest number of cupcakes in each box. How many cupcakes will be in each box?
We should find the GCF of 27 and 125 GCF of 27 and 125 is 1.
There will be 1 cupcake in each box.
Explanation
As the GCF of 27 and 125 is 1, the baker can only pack 1 cupcake in each box.
Problem 2
A gardener has 27 rose bushes and 125 tulip bulbs. She wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 27 and 125 is 1.
So each row will have 1 plant.
Explanation
There are 27 rose bushes and 125 tulip bulbs.
To find the total number of plants in each row, we should find the GCF of 27 and 125.
There will be 1 plant in each row.
Problem 3
A chef has 27 grams of sugar and 125 grams of flour. She wants to divide both into portions of equal weight, using the largest possible weight. What should be the weight of each portion?
To calculate the largest equal weight, we have to calculate the GCF of 27 and 125.
The GCF of 27 and 125 is 1.
The weight of each portion is 1 gram.
Explanation
For calculating the largest weight of the portions, we first need to calculate the GCF of 27 and 125, which is 1.
The weight of each portion will be 1 gram.
Problem 4
A tailor has two pieces of fabric, one 27 meters long and the other 125 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric GCF of 27 and 125 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two pieces of fabric, 27 meters and 125 meters, respectively.
We have to find the GCF of 27 and 125, which is 1 meter.
The longest length of each piece is 1 meter.
Problem 5
If the GCF of 27 and โbโ is 1, and the LCM is 3375, find โbโ.
The value of ‘b’ is 125.
Explanation
GCF x LCM = product of the numbers
1 × 3375 = 27 × b
3375 = 27b
b = 3375 ÷ 27 = 125
FAQs on the Greatest Common Factor of 27 and 125
1.What is the LCM of 27 and 125?
2.Is 27 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 125?
5.Are 27 and 125 prime numbers?
Important Glossaries for GCF of 27 and 125
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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 27 are 3.
- Euclidean Algorithm: A method for finding the greatest common divisor (GCD) of two numbers by using division and remainder.
- Co-prime: Two numbers are co-prime if their greatest common factor (GCF) is 1.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 27 and 125 is 3375.
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.
