GCF of 48 and 27
2026-02-28 17:58 Diff
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Last updated on September 24, 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 48 and 27.

What is the GCF of 48 and 27?

The greatest common factor of 48 and 27 is 3. 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 48 and 27?

To find the GCF of 48 and 27, a few methods are described below -

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm

GCF of 48 and 27 by Using Listing of Factors

Steps to find the GCF of 48 and 27 using the listing of factors

Step 1: Firstly, list the factors of each number

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

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

Step 2: Now, identify the common factors of them Common factors of 48 and 27: 1, 3.

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

The GCF of 48 and 27 is 3.

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GCF of 48 and 27 Using Prime Factorization

To find the GCF of 48 and 27 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 48: 48 = 2 x 2 x 2 x 2 x 3 = 24 x 3

Prime Factors of 27: 27 = 3 x 3 x 3 = 33

Step 2: Now, identify the common prime factors The common prime factor is: 3

Step 3: Multiply the common prime factors 3 = 3. The Greatest Common Factor of 48 and 27 is 3.

GCF of 48 and 27 Using Division Method or Euclidean Algorithm Method

Find the GCF of 48 and 27 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 48 by 27 48 ÷ 27 = 1 (quotient), The remainder is calculated as 48 − (27×1) = 21 The remainder is 21, not zero, so continue the process

Step 2: Now divide the previous divisor (27) by the previous remainder (21) Divide 27 by 21 27 ÷ 21 = 1 (quotient), remainder = 27 − (21×1) = 6 Continue with the next step

Step 3: Divide the previous divisor (21) by the previous remainder (6) 21 ÷ 6 = 3 (quotient), remainder = 21 − (6×3) = 3

Step 4: Divide the previous divisor (6) by the previous remainder (3) 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0

The remainder is zero, the divisor will become the GCF. The GCF of 48 and 27 is 3.

Common Mistakes and How to Avoid Them in GCF of 48 and 27

Finding GCF of 48 and 27 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 baker has 48 cookies and 27 cupcakes. She wants to pack them into boxes with the same number of pastries in each box, with the largest number of items per box. How many items will be in each box?

Okay, lets begin

We should find the GCF of 48 and 27. GCF of 48 and 27: 3.

There are 3 equal groups. 48 ÷ 3 = 16 27 ÷ 3 = 9

There will be 3 groups, and each group gets 16 cookies and 9 cupcakes.

Explanation

As the GCF of 48 and 27 is 3, the baker can make 3 groups.

Now divide 48 and 27 by 3. Each group gets 16 cookies and 9 cupcakes.

Well explained 👍

Problem 2

A gardener has 48 roses and 27 tulips. She wants to arrange them in bouquets with the same number of flowers in each bouquet, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?

Okay, lets begin

GCF of 48 and 27: 3. So each bouquet will have 3 flowers.

Explanation

There are 48 roses and 27 tulips. To find the total number of flowers in each bouquet, we should find the GCF of 48 and 27.

There will be 3 flowers in each bouquet.

Well explained 👍

Problem 3

A tailor has 48 meters of silk fabric and 27 meters of linen 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 48 and 27.

The GCF of 48 and 27: 3. Each piece of fabric is 3 meters long.

Explanation

For calculating the longest length of the fabric, first, we need to calculate the GCF of 48 and 27, which is 3.

The length of each piece of fabric will be 3 meters.

Well explained 👍

Problem 4

A woodworker has two wooden boards, one 48 cm long and the other 27 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 woodworker needs the longest piece of wood. GCF of 48 and 27: 3. The longest length of each piece is 3 cm.

Explanation

To find the longest length of each piece of the two wooden boards, 48 cm and 27 cm, respectively,

we have to find the GCF of 48 and 27, which is 3 cm.

The longest length of each piece is 3 cm.

Well explained 👍

Problem 5

If the GCF of 48 and ‘b’ is 3, and the LCM is 432. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 27.

Explanation

GCF x LCM = product of the numbers

3 × 432 = 48 × b

1296 = 48b

b = 1296 ÷ 48 = 27

Well explained 👍

FAQs on the Greatest Common Factor of 48 and 27

1.What is the LCM of 48 and 27?

The LCM of 48 and 27 is 432.

2.Is 48 divisible by 2?

Yes, 48 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 27?

The prime factorization of 27 is 3^3.

5.Are 48 and 27 prime numbers?

No, 48 and 27 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 48 and 27

  • 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 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 21 are 3 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 17 is divided by 5, the remainder is 2 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 27 is 432.

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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.