GCF of 72 and 18
2026-02-28 11:44 Diff
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Last updated on September 19, 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 to schedule events. In this topic, we will learn about the GCF of 72 and 18.

What is the GCF of 72 and 18?

The greatest common factor of 72 and 18 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.

How to find the GCF of 72 and 18?

To find the GCF of 72 and 18, a few methods are described below 

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 72 and 18 by Using Listing of Factors

Steps to find the GCF of 72 and 18 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Factors of 18 = 1, 2, 3, 6, 9, 18.

Step 2: Now, identify the common factors of them Common factors of 72 and 18: 1, 2, 3, 6, 9, 18.

Step 3: Choose the largest factor The largest factor that both numbers have is 18.

The GCF of 72 and 18 is 18.

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GCF of 72 and 18 Using Prime Factorization

To find the GCF of 72 and 18 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²

Step 2: Now, identify the common prime factors

The common prime factors are: 2 × 3² = 2 × 9

Step 3: Multiply the common prime factors 2 × 3² = 2 × 9 = 18.

The Greatest Common Factor of 72 and 18 is 18.

GCF of 72 and 18 Using Division Method or Euclidean Algorithm Method

Find the GCF of 72 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 72 by 18 72 ÷ 18 = 4 (quotient),

The remainder is calculated as 72 − (18×4) = 0

The remainder is zero, so the divisor will become the GCF.

The GCF of 72 and 18 is 18.

Common Mistakes and How to Avoid Them in GCF of 72 and 18

Finding GCF of 72 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A chef has 72 apples and 18 pears. He wants to create fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?

Okay, lets begin

We should find GCF of 72 and 18 GCF of 72 and 18 2 × 3² = 2 × 9 = 18.

There are 18 equal baskets 72 ÷ 18 = 4 18 ÷ 18 = 1

There will be 18 baskets, and each basket gets 4 apples and 1 pear.

Explanation

As the GCF of 72 and 18 is 18, the chef can make 18 baskets.

Now divide 72 and 18 by 18.

Each basket gets 4 apples and 1 pear.

Well explained 👍

Problem 2

A company has 72 black chairs and 18 white chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?

Okay, lets begin

GCF of 72 and 18 2 × 3² = 2 × 9 = 18.

So each row will have 18 chairs.

Explanation

There are 72 black and 18 white chairs.

To find the total number of chairs in each row, we should find the GCF of 72 and 18.

There will be 18 chairs in each row.

Well explained 👍

Problem 3

A farmer has 72 meters of fencing for his apple orchard and 18 meters of fencing for his pear orchard. He wants to cut both lengths of fencing into pieces of equal length, using the longest possible length. What should be the length of each piece?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 72 and 18

The GCF of 72 and 18 2 × 3² = 2 × 9 = 18.

The fencing is 18 meters long.

Explanation

For calculating the longest length of the fencing first we need to calculate the GCF of 72 and 18, which is 18.

The length of each piece of the fencing will be 18 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 72 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 72 and 18 2 × 3² = 2 × 9 = 18.

The longest length of each piece is 18 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 72 cm and 18 cm, respectively, we have to find the GCF of 72 and 18, which is 18 cm.

The longest length of each piece is 18 cm.

Well explained 👍

Problem 5

If the GCF of 72 and ‘b’ is 18, and the LCM is 216. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 54.

Explanation

GCF × LCM = product of the numbers

18 × 216 = 72 × b

3888 = 72b

b = 3888 ÷ 72 = 54

Well explained 👍

FAQs on the Greatest Common Factor of 72 and 18

1.What is the LCM of 72 and 18?

The LCM of 72 and 18 is 72.

2.Is 72 divisible by 2?

Yes, 72 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 18?

The prime factorization of 18 is 2 × 3².

5.Are 72 and 18 prime numbers?

No, 72 and 18 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 72 and 18

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
  • 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, 15, 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 72 are 2 and 3.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 72 and 18 is 72.

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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.