Last updated on August 1st, 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 9 and 12.
The greatest common factor of 9 and 12 is 3. 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 9 and 12, a few methods are described below
Steps to find the GCF of 9 and 12 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 9 = 1, 3, 9. Factors of 12 = 1, 2, 3, 4, 6, 12.
Step 2: Now, identify the common factors of them Common factors of 9 and 12: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3.
The GCF of 9 and 12 is 3.
To find the GCF of 9 and 12 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 9: 9 = 3 x 3 = 3²
Prime Factors of 12: 12 = 2 x 2 x 3 = 2² x 3
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3
The Greatest Common Factor of 9 and 12 is 3.
Find the GCF of 9 and 12 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 12 by 9 12 ÷ 9 = 1 (quotient),
The remainder is calculated as 12 − (9×1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (9) by the previous remainder (3)
Divide 9 by 3 9 ÷ 3 = 3 (quotient), remainder = 9 − (3×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 9 and 12 is 3.
Finding GCF of 9 and 12 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A teacher has 9 markers and 12 notebooks. 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 9 and 12 GCF of 9 and 12 3
There are 3 equal groups 9 ÷ 3 = 3 12 ÷ 3 = 4
There will be 3 groups, and each group gets 3 markers and 4 notebooks.
As the GCF of 9 and 12 is 3, the teacher can make 3 groups.
Now divide 9 and 12 by 3.
Each group gets 3 markers and 4 notebooks.
A school has 9 green chairs and 12 yellow 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?
GCF of 9 and 12 3 So each row will have 3 chairs.
There are 9 green and 12 yellow chairs.
To find the total number of chairs in each row, we should find the GCF of 9 and 12.
There will be 3 chairs in each row.
A tailor has 9 meters of silk ribbon and 12 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 9 and 12
The GCF of 9 and 12 3
The ribbon is 3 meters long.
For calculating the longest length of the ribbon first we need to calculate the GCF of 9 and 12, which is 3.
The length of each piece of the ribbon will be 3 meters.
A carpenter has two wooden planks, one 9 cm long and the other 12 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 9 and 12 3 The longest length of each piece is 3 cm.
To find the longest length of each piece of the two wooden planks, 9 cm and 12 cm, respectively.
We have to find the GCF of 9 and 12, which is 3 cm.
The longest length of each piece is 3 cm.
If the GCF of 9 and ‘a’ is 3, and the LCM is 36. Find ‘a’.
The value of ‘a’ is 12.
GCF x LCM = product of the numbers 3 × 36 = 9 × a
108 = 9a
a = 108 ÷ 9 = 12
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.