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 60 and 72.
The greatest common factor of 60 and 72 is 12. 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 60 and 72, a few methods are described below:
Steps to find the GCF of 60 and 72 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
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 60 and 72: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 12.
The GCF of 60 and 72 is 12.
To find the GCF of 60 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 22 x 3 x 5
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: 2 x 2 x 3 = 22 x 3
Step 3: Multiply the common prime factors:
22 x 3 = 4 x 3 = 12.
The Greatest Common Factor of 60 and 72 is 12.
Find the GCF of 60 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 60 72 ÷ 60 = 1 (quotient), The remainder is calculated as 72 − (60×1) = 12
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (60) by the previous remainder (12)
Divide 60 by 12 60 ÷ 12 = 5 (quotient), remainder = 60 − (12×5) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 60 and 72 is 12.
Finding the GCF of 60 and 72 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A chef has 60 apples and 72 oranges. She wants to pack them into the largest possible equal sets. How many pieces of fruit will be in each set?
We should find the GCF of 60 and 72 GCF of 60 and 72
22 x 3 = 4 x 3 = 12.
There are 12 equal sets
60 ÷ 12 = 5
72 ÷ 12 = 6
There will be 12 sets, and each set gets 5 apples and 6 oranges.
As the GCF of 60 and 72 is 12, the chef can make 12 sets.
Now divide 60 and 72 by 12.
Each set gets 5 apples and 6 oranges.
A gardener has 60 red roses and 72 yellow roses. He wants to arrange them in bouquets with the same number of roses in each bouquet, using the largest possible number of roses per bouquet. How many roses will be in each bouquet?
GCF of 60 and 72
22 x 3 = 4 × 3 = 12.
So each bouquet will have 12 roses.
There are 60 red and 72 yellow roses.
To find the total number of roses in each bouquet, we should find the GCF of 60 and 72.
There will be 12 roses in each bouquet.
A tailor has 60 meters of red fabric and 72 meters of blue 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?
For calculating the longest equal length, we have to calculate the GCF of 60 and 72.
The GCF of 60 and 72
22 x 3 = 4 × 3 = 12.
The fabric is 12 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 60 and 72, which is 12.
The length of each piece of the fabric will be 12 meters.
A carpenter has two wooden planks, one 60 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 60 and 72
22 x 3 = 4 × 3 = 12.
The longest length of each piece is 12 cm.
To find the longest length of each piece of the two wooden planks, 60 cm and 72 cm, respectively, we have to find the GCF of 60 and 72, which is 12 cm. The longest length of each piece is 12 cm.
If the GCF of 60 and ‘b’ is 12, and the LCM is 360. Find ‘b’.
The value of ‘b’ is 72.
GCF x LCM = product of the numbers
12 × 360 = 60 × b
4320 = 60b
b = 4320 ÷ 60 = 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.