Last updated on July 31st, 2025
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 18 and 54.
The greatest common factor of 18 and 54 is 18. 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.
To find the GCF of 18 and 54, a few methods are described below:
Steps to find the GCF of 18 and 54 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them.
Common factors of 18 and 54: 1, 2, 3, 6, 9, 18.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 18.
The GCF of 18 and 54 is 18.
To find the GCF of 18 and 54 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime Factors of each number
Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²
Prime Factors of 54: 54 = 2 × 3 × 3 × 3 = 2 × 3³
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 × 3²
Step 3: Multiply the common prime factors
2 × 3² = 2 × 9 = 18.
The Greatest Common Factor of 18 and 54 is 18.
Find the GCF of 18 and 54 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 54 by 18 54 ÷ 18 = 3 (quotient), The remainder is calculated as 54 − (18×3) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 18 and 54 is 18.
Finding GCF of 18 and 54 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A chef has 18 apples and 54 oranges. She wants to arrange them into fruit baskets with the largest number of fruits in each basket. How many fruits will be in each basket?
We should find GCF of 18 and 54 GCF of 18 and 54
2 × 3² = 18.
There are 18 fruits in each basket.
18 ÷ 18 = 1
54 ÷ 18 = 3
There will be 3 baskets, each with 1 apple and 3 oranges.
As the GCF of 18 and 54 is 18, the chef can make 3 baskets.
Now divide 18 and 54 by 18.
Each basket gets 1 apple and 3 oranges.
A school has 18 red flags and 54 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 18 and 54
2 × 3² = 18.
So each row will have 18 flags.
There are 18 red and 54 blue flags.
To find the total number of flags in each row, we should find the GCF of 18 and 54.
There will be 18 flags in each row.
A gardener has 18 meters of red hose and 54 meters of green hose. She wants to cut both hoses 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 18 and 54
The GCF of 18 and 54
2 × 3² = 18.
The hose is 18 meters long.
For calculating the longest length of the hose first, we need to calculate the GCF of 18 and 54, which is 18. The length of each piece of the hose will be 18 meters.
A carpenter has two wooden planks, one 18 cm long and the other 54 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 18 and 54
2 × 3² = 18.
The longest length of each piece is 18 cm.
To find the longest length of each piece of the two wooden planks, 18 cm and 54 cm, respectively.
We have to find the GCF of 18 and 54, which is 18 cm.
The longest length of each piece is 18 cm.
If the GCF of 18 and ‘b’ is 18, and the LCM is 54. Find ‘b’.
The value of ‘b’ is 54.
GCF × LCM = product of the numbers
18 × 54 = 18 × b
972 = 18b
b = 972 ÷ 18 = 54
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.
: She loves to read number jokes and games.