100 LearnersLast updated on August 14th, 2025
GCF of 54 and 250
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 54 and 250.
What is the GCF of 54 and 250?
The greatest common factor of 54 and 250 is 2. 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 54 and 250?
To find the GCF of 54 and 250, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 54 and 250 by Using Listing of factors
Steps to find the GCF of 54 and 250 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Factors of 250 = 1, 2, 5, 10, 25, 50, 125, 250.
Step 2: Now, identify the common factors of them Common factors of 54 and 250: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2. The GCF of 54 and 250 is 2.
GCF of 54 and 250 Using Prime Factorization
To find the GCF of 54 and 250 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 54: 54 = 2 × 3 × 3 × 3 = 2 × 3³
Prime Factors of 250: 250 = 2 × 5 × 5 × 5 = 2 × 5³
Step 2: Now, identify the common prime factors The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2. The Greatest Common Factor of 54 and 250 is 2.
GCF of 54 and 250 Using Division Method or Euclidean Algorithm Method
Find the GCF of 54 and 250 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 250 by 54 250 ÷ 54 = 4 (quotient), The remainder is calculated as 250 − (54×4) = 34
The remainder is 34, not zero, so continue the process
Step 2: Now divide the previous divisor (54) by the previous remainder (34) Divide 54 by 34 54 ÷ 34 = 1 (quotient), remainder = 54 − (34×1) = 20
Step 3: Divide the previous divisor (34) by the previous remainder (20) 34 ÷ 20 = 1 (quotient), remainder = 34 − (20×1) = 14
Step 4: Divide the previous divisor (20) by the previous remainder (14) 20 ÷ 14 = 1 (quotient), remainder = 20 − (14×1) = 6
Step 5: Divide the previous divisor (14) by the previous remainder (6) 14 ÷ 6 = 2 (quotient), remainder = 14 − (6×2) = 2
Step 6: Divide the previous divisor (6) by the previous remainder (2) 6 ÷ 2 = 3 (quotient), remainder = 6 − (2×3) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 54 and 250 is 2.
Common Mistakes and How to Avoid Them in GCF of 54 and 250
Finding GCF of 54 and 250 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 54, students may mention 7 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 an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true that a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 54 and 250 Examples
Problem 1
A chef has 54 apples and 250 oranges. She wants to create fruit baskets with each basket having the same number of fruits. What is the maximum number of fruits in each basket?
We should find GCF of 54 and 250 GCF of 54 and 250 2. There are 2 equal fruits in each basket.
Explanation
As the GCF of 54 and 250 is 2, the chef can make baskets with 2 fruits each.
Problem 2
A gardener has 54 roses and 250 tulips. He wants to plant them in rows with the same number of flowers in each row. What is the largest number of flowers he can plant in each row?
GCF of 54 and 250 2. So each row will have 2 flowers.
Explanation
There are 54 roses and 250 tulips. To find the total number of flowers in each row, we should find the GCF of 54 and 250. There will be 2 flowers in each row.
Problem 3
A tailor has 54 meters of silk and 250 meters of cotton. She wants to cut both fabrics 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 54 and 250 The GCF of 54 and 250 2. The fabric is 2 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 54 and 250 which is 2. The length of each piece of fabric will be 2 meters.
Problem 4
A carpenter has two wooden planks, one 54 cm long and the other 250 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 54 and 250 2. The longest length of each piece is 2 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 54 cm and 250 cm, respectively. We have to find the GCF of 54 and 250, which is 2 cm. The longest length of each piece is 2 cm.
Problem 5
If the GCF of 54 and ‘b’ is 2, and the LCM is 6750, find ‘b’.
The value of ‘b’ is 250.
Explanation
GCF × LCM = product of the numbers
2 × 6750 = 54 × b
13500 = 54b
b = 13500 ÷ 54 = 250
FAQs on the Greatest Common Factor of 54 and 250
1.What is the LCM of 54 and 250?
2.Is 54 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 250?
5.Are 54 and 250 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 54 and 250?
7.What are some fun ways kids in Canada can practice GCF of 54 and 250 with numbers?
8.What role do numbers and GCF of 54 and 250 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 54 and 250 skills?
Important Glossaries for GCF of 54 and 250
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 54 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 54 is divided by 7, the remainder is 5 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 54 and 250 is 6750.
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.
