GCF of 48 and 84
2026-02-21 20:37 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 items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 48 and 84.

What is the GCF of 48 and 84?

The greatest common factor of 48 and 84 is 12. The largest divisor of two or more numbers is called the GCF of the numbers. 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 84?

To find the GCF of 48 and 84, a few methods are described below 

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

GCF of 48 and 84 by Using Listing of factors

Steps to find the GCF of 48 and 84 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 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Step 2: Now, identify the common factors Common factors of 48 and 84: 1, 2, 3, 4, 6, 12.

Step 3: Choose the largest factor The largest factor that both numbers have is 12.

The GCF of 48 and 84 is 12.

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GCF of 48 and 84 Using Prime Factorization

To find the GCF of 48 and 84 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 84: 84 = 2 x 2 x 3 x 7 = 22 x 3 x 7

Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 = 22 x 3

Step 3: Multiply the common prime factors 22 x 3 = 4 × 3 = 12. The Greatest Common Factor of 48 and 84 is 12.

GCF of 48 and 84 Using Division Method or Euclidean Algorithm Method

Find the GCF of 48 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 84 by 48 84 ÷ 48 = 1 (quotient),

The remainder is calculated as 84 − (48×1) = 36 The remainder is 36, not zero, so continue the process

Step 2: Now divide the previous divisor (48) by the previous remainder (36)

Divide 48 by 36 48 ÷ 36 = 1 (quotient), remainder = 48 − (36×1) = 12

Step 3: Now divide the previous divisor (36) by the previous remainder (12) 36 ÷ 12 = 3 (quotient), remainder = 36 − (12×3) = 0 The remainder is zero, the divisor will become the GCF.

The GCF of 48 and 84 is 12.

Common Mistakes and How to Avoid Them in GCF of 48 and 84

Finding the GCF of 48 and 84 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 48 notebooks and 84 markers. 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 48 and 84 GCF of 48 and 84 22 x 3 = 4 x 3 = 12.

There are 12 equal groups 48 ÷ 12 = 4 84 ÷ 12 = 7

There will be 12 groups, and each group gets 4 notebooks and 7 markers.

Explanation

As the GCF of 48 and 84 is 12, the teacher can make 12 groups.

Now divide 48 and 84 by 12.

Each group gets 4 notebooks and 7 markers.

Well explained 👍

Problem 2

A school has 48 red chairs and 84 blue 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 48 and 84 2^2 x 3 = 4 × 3 = 12.

So each row will have 12 chairs.

Explanation

There are 48 red and 84 blue chairs.

To find the total number of chairs in each row, we should find the GCF of 48 and 84.

There will be 12 chairs in each row.

Well explained 👍

Problem 3

A tailor has 48 meters of red ribbon and 84 meters of blue 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 48 and 84

The GCF of 48 and 84 22 x 3 = 4 × 3 = 12.

The ribbon is 12 meters long.

Explanation

For calculating the longest length of the ribbon first, we need to calculate the GCF of 48 and 84, which is 12.

The length of each piece of the ribbon will be 12 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 48 cm long and the other 84 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 48 and 84 22 x 3 = 4 × 3 = 12.

The longest length of each piece is 12 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 48 cm and 84 cm, respectively, we have to find the GCF of 48 and 84, which is 12 cm.

The longest length of each piece is 12 cm.

Well explained 👍

Problem 5

If the GCF of 48 and ‘a’ is 12, and the LCM is 336. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 84.

Explanation

GCF x LCM = product of the numbers

12 × 336 = 48 × a

4032 = 48a

a = 4032 ÷ 48 = 84

Well explained 👍

FAQs on the Greatest Common Factor of 48 and 84

1.What is the LCM of 48 and 84?

The LCM of 48 and 84 is 336.

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 84?

The prime factorization of 84 is 22 x 3 x 7.

5.Are 48 and 84 prime numbers?

No, 48 and 84 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 48 and 84

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 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 15 are 3 and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 48 and 84 is 336.

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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.