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 items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 48 and 72.
The greatest common factor of 48 and 72 is 24. 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 48 and 72, a few methods are described below -
Steps to find the GCF of 48 and 72 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 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 48 and 72: 1, 2, 3, 4, 6, 8, 12, 24.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 24.
The GCF of 48 and 72 is 24.
To find the GCF of 48 and 72 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 = 2^4 x 3
Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 2^3 x 3^2
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 2 x 2 x 3 = 2^3 x 3
Step 3: Multiply the common prime factors.
2^3 x 3 = 8 x 3 = 24.
The Greatest Common Factor of 48 and 72 is 24.
Find the GCF of 48 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 48. 72 ÷ 48 = 1 (quotient),
The remainder is calculated as 72 − (48 x 1) = 24.
The remainder is 24, not zero, so continue the process.
Step 2: Now divide the previous divisor (48) by the previous remainder (24).
Divide 48 by 24. 48 ÷ 24 = 2 (quotient), remainder = 48 − (24 x 2) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 48 and 72 is 24.
Finding the GCF of 48 and 72 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
A gardener has 48 tulips and 72 roses. She wants to create bouquets with the largest possible number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 48 and 72.
GCF of 48 and 72 2^3 x 3 = 8 x 3 = 24.
There are 24 flowers in each bouquet. 48 ÷ 24 = 2 72 ÷ 24 = 3
There will be 24 bouquets, and each bouquet gets 2 tulips and 3 roses.
As the GCF of 48 and 72 is 24, the gardener can make 24 bouquets.
Now divide 48 and 72 by 24.
Each bouquet gets 2 tulips and 3 roses.
A school wants to arrange 48 red flags and 72 blue flags in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 48 and 72 2^3 x 3 = 8 x 3 = 24. So each row will have 24 flags.
There are 48 red and 72 blue flags.
To find the total number of flags in each row, we should find the GCF of 48 and 72.
There will be 24 flags in each row.
A chef has 48 meters of pasta and 72 meters of sausage. She wants to cut both 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 48 and 72.
The GCF of 48 and 72
2^3 x 3 = 8 x 3 = 24.
The length of each piece is 24 meters.
To calculate the longest length of the pasta and sausage, first, we need to calculate the GCF of 48 and 72, which is 24.
The length of each piece of pasta and sausage will be 24 meters.
A carpenter has two wooden planks, one 48 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?
The carpenter needs the longest piece of wood.
GCF of 48 and 72
2^3 x 3 = 8 x 3 = 24.
The longest length of each piece is 24 cm.
To find the longest length of each piece of the two wooden planks, 48 cm and 72 cm, respectively, we have to find the GCF of 48 and 72, which is 24 cm.
The longest length of each piece is 24 cm.
If the GCF of 48 and ‘a’ is 24, and the LCM is 144, find ‘a’.
The value of ‘a’ is 72.
GCF x LCM = product of the numbers 24 x 144 = 48 x a
3456 = 48a
a = 3456 ÷ 48 = 72
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.