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 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.
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.
To find the GCF of 27 and 72, a few methods are described below:
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.
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.
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.
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.
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?
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.
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.
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?
GCF of 27 and 72 3² = 9. So each row will have 9 apples.
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.
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?
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.
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.
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?
The carpenter needs the longest piece of wood GCF of 27 and 72 3² = 9.
The longest length of each piece is 9 cm.
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.
If the GCF of 27 and ‘b’ is 9, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 72.
GCF x LCM = product of the numbers
9 × 216 = 27 × b
1944 = 27b
b = 1944 ÷ 27 = 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.