GCF of 27 and 72
2026-02-28 01:11 Diff
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Last updated on August 5, 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 27 and 72.

What is the GCF of 27 and 72?

The greatest common factor of 27 and 72 is 9. 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 27 and 72?

To find the GCF of 27 and 72, a few methods are described below:

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

GCF of 27 and 72 by Using Listing of Factors

Steps to find the GCF of 27 and 72 using the listing of factors:

Step 1: Firstly, list the factors of each number

Factors of 27 = 1, 3, 9, 27.

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

Step 2: Now, identify the common factors of them Common factors of 27 and 72: 1, 3, 9.

Step 3: Choose the largest factor The largest factor that both numbers have is 9.

The GCF of 27 and 72 is 9.

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GCF of 27 and 72 Using Prime Factorization

To find the GCF of 27 and 72 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 72: 72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²

Step 2: Now, identify the common prime factors

The common prime factors are: 3 x 3 = 3²

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

The Greatest Common Factor of 27 and 72 is 9.

GCF of 27 and 72 Using Division Method or Euclidean Algorithm Method

Find the GCF of 27 and 72 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 27 72 ÷ 27 = 2 (quotient),

The remainder is calculated as 72 − (27×2) = 18

The remainder is 18, not zero, so continue the process

Step 2: Now divide the previous divisor (27) by the previous remainder (18)

Divide 27 by 18 27 ÷ 18 = 1 (quotient), remainder = 27 − (18×1) = 9

Step 3: Now divide the previous divisor (18) by the previous remainder (9)

Divide 18 by 9 18 ÷ 9 = 2 (quotient), remainder = 18 − (9×2) = 0

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

The GCF of 27 and 72 is 9.

Common Mistakes and How to Avoid Them in GCF of 27 and 72

Finding the GCF of 27 and 72 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A teacher has 27 notebooks and 72 pens. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 27 and 72 GCF of 27 and 72 3² = 9.

There are 9 equal groups.

27 ÷ 9 = 3

72 ÷ 9 = 8

There will be 9 groups, and each group gets 3 notebooks and 8 pens.

Explanation

As the GCF of 27 and 72 is 9, the teacher can make 9 groups.

Now divide 27 and 72 by 9.

Each group gets 3 notebooks and 8 pens.

Well explained 👍

Problem 2

A school has 27 red apples and 72 green apples. They want to arrange them in rows with the same number of apples in each row, using the largest possible number of apples per row. How many apples will be in each row?

Okay, lets begin

GCF of 27 and 72 3² = 9. So each row will have 9 apples.

Explanation

There are 27 red and 72 green apples.

To find the total number of apples in each row, we should find the GCF of 27 and 72.

There will be 9 apples in each row.

Well explained 👍

Problem 3

A tailor has 27 meters of silk ribbon and 72 meters of cotton ribbon. She wants to cut both ribbons 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 27 and 72

The GCF of 27 and 72 3² = 9.

The ribbon is 9 meters long.

Explanation

For calculating the longest length of the ribbon, first, we need to calculate the GCF of 27 and 72, which is 9. The length of each piece of the ribbon will be 9 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 27 cm long and the other 72 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 27 and 72 3² = 9.

The longest length of each piece is 9 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 27 cm and 72 cm, respectively, we have to find the GCF of 27 and 72, which is 9 cm. The longest length of each piece is 9 cm.

Well explained 👍

Problem 5

If the GCF of 27 and ‘b’ is 9, and the LCM is 216. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 72.

Explanation

GCF x LCM = product of the numbers

9 × 216 = 27 × b

1944 = 27b

b = 1944 ÷ 27 = 72

Well explained 👍

FAQs on the Greatest Common Factor of 27 and 72

1.What is the LCM of 27 and 72?

The LCM of 27 and 72 is 216.

2.Is 27 divisible by 3?

Yes, 27 is divisible by 3 because the sum of its digits (2+7) equals 9, which is divisible by 3.

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 72?

The prime factorization of 72 is 2³ x 3².

5.Are 27 and 72 prime numbers?

No, 27 and 72 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 27 and 72

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
  • 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, 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 18 are 2 and 3².
  • 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 27 and 72 is 216.
  • GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 27 and 72 will be 9, as it is their largest common factor that divides the numbers completely.

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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.