Last updated on August 5th, 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 6 and 18.
The greatest common factor of 6 and 18 is 6. 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 6 and 18, a few methods are described below:
Steps to find the GCF of 6 and 18 using the listing of factors:
Step 1: First, list the factors of each number
Factors of 6 = 1, 2, 3, 6.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Step 2: Now, identify the common factors of them Common factors of 6 and 18: 1, 2, 3, 6.
Step 3: Choose the largest factor The largest factor that both numbers have is 6.
The GCF of 6 and 18 is 6.
To find the GCF of 6 and 18 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 6: 6 = 2 × 3
Prime Factors of 18: 18 = 2 × 3 × 3
Step 2: Now, identify the common prime factors
The common prime factors are: 2 × 3
Step 3: Multiply the common prime factors 2 × 3 = 6.
The Greatest Common Factor of 6 and 18 is 6.
Find the GCF of 6 and 18 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 18 by 6 18 ÷ 6 = 3 (quotient), remainder = 18 − (6×3) = 0
Step 2: Since the remainder is zero, the divisor will become the GCF.
The GCF of 6 and 18 is 6.
Finding GCF of 6 and 18 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 6 kilograms of flour and 18 kilograms of sugar. He wants to divide them into equal portions with the largest possible number of grams in each portion. How many grams will be in each portion?
We should find the GCF of 6 and 18 GCF of 6 and 18 is 6.
There are 6 equal portions
6 kg ÷ 6 = 1 kg
18 kg ÷ 6 = 3 kg
Each portion will have 1 kilogram of flour and 3 kilograms of sugar.
As the GCF of 6 and 18 is 6, the chef can make 6 portions.
Now divide 6 and 18 by 6.
Each portion gets 1 kilogram of flour and 3 kilograms of sugar.
A gardener has 6 rose bushes and 18 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 6 and 18 is 6. So each row will have 6 plants.
There are 6 rose bushes and 18 tulip bulbs.
To find the total number of plants in each row, we should find the GCF of 6 and 18.
There will be 6 plants in each row.
A tailor has 6 meters of red fabric and 18 meters of blue fabric. 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 6 and 18.
The GCF of 6 and 18 is 6.
The fabric is 6 meters long.
For calculating the longest length of the fabric, we first need to calculate the GCF of 6 and 18, which is 6.
The length of each piece of the fabric will be 6 meters.
A carpenter has two wooden planks, one 6 cm long and the other 18 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 6 and 18 is 6. The longest length of each piece is 6 cm.
To find the longest length of each piece of the two wooden planks, 6 cm and 18 cm respectively, we have to find the GCF of 6 and 18, which is 6 cm. The longest length of each piece is 6 cm.
If the GCF of 6 and ‘b’ is 6, and the LCM is 18, find ‘b’.
The value of ‘b’ is 18.
GCF × LCM = product of the numbers
6 × 18 = 6 × b
108 = 6b
b = 108 ÷ 6 = 18
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.