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 schedule events. In this topic, we will learn about the GCF of 36 and 27.
The greatest common factor of 36 and 27 is 9. 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.
To find the GCF of 36 and 27, a few methods are described below:
Steps to find the GCF of 36 and 27 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 27 = 1, 3, 9, 27.
Step 2: Now, identify the common factors Common factors of 36 and 27: 1, 3, 9.
Step 3: Choose the largest factor
The largest factor that both numbers have is 9.
The GCF of 36 and 27 is 9.
To find the GCF of 36 and 27 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Prime Factors of 27: 27 = 3 x 3 x 3 = 3³
Step 2: 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 36 and 27 is 9.
Find the GCF of 36 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 36 by 27 36 ÷ 27 = 1 (quotient),
The remainder is calculated as 36 − (27 x 1) = 9
The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (27) by the previous remainder (9)
Divide 27 by 9 27 ÷ 9 = 3 (quotient), remainder = 27 − (9 x 3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 36 and 27 is 9.
Finding GCF of 36 and 27 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 36 apples and 27 oranges. She wants to create fruit baskets with the largest number of fruits in each basket, ensuring each basket is identical. How many fruits will be in each basket?
We should find the GCF of 36 and 27.
GCF of 36 and 27: 3² = 9.
There are 9 equal groups. 36 ÷ 9 = 4 27 ÷ 9 = 3
There will be 9 baskets, and each basket gets 4 apples and 3 oranges.
As the GCF of 36 and 27 is 9, the chef can make 9 baskets. Now divide 36 and 27 by 9. Each basket gets 4 apples and 3 oranges.
A company has 36 brochures and 27 flyers. They want to distribute them in packets with the same number of items in each packet, using the largest possible number of items per packet. How many items will be in each packet?
GCF of 36 and 27: 3² = 9.
So each packet will have 9 items.
There are 36 brochures and 27 flyers. To find the total number of items in each packet, we should find the GCF of 36 and 27. There will be 9 items in each packet.
A gardener has 36 tulip bulbs and 27 daffodil bulbs. She wants to plant them in rows with the same number of bulbs in each row, using the longest possible row length. How many bulbs should be in each row?
For calculating the longest equal row length, we have to calculate the GCF of 36 and 27.
The GCF of 36 and 27: 3² = 9.
Each row is 9 bulbs long.
For calculating the longest row length, we first need to calculate the GCF of 36 and 27, which is 9. The length of each row of bulbs will be 9.
A builder has two steel rods, one 36 cm long and the other 27 cm long. He wants to cut them into the longest possible equal pieces, without any steel left over. What should be the length of each piece?
The builder needs the longest piece of steel.
GCF of 36 and 27: 3² = 9.
The longest length of each piece is 9 cm.
To find the longest length of each piece of the two steel rods, 36 cm and 27 cm, respectively, we have to find the GCF of 36 and 27, which is 9 cm. The longest length of each piece is 9 cm.
If the GCF of 36 and ‘b’ is 9, and the LCM is 108, find ‘b’.
The value of ‘b’ is 27.
GCF x LCM = product of the numbers 9 × 108 = 36 × b
972 = 36b
b = 972 ÷ 36 = 27
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.