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 schedule events. In this topic, we will learn about the GCF of 9 and 21.
The greatest common factor of 9 and 21 is 3. 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 9 and 21, a few methods are described below:
Steps to find the GCF of 9 and 21 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 9 = 1, 3, 9.
Factors of 21 = 1, 3, 7, 21.
Step 2: Now, identify the common factors. Common factors of 9 and 21: 1, 3.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 3.
The GCF of 9 and 21 is 3.
To find the GCF of 9 and 21 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 21: 21 = 3 x 7
Step 2: Now, identify the common prime factors.
The common prime factor is: 3
Step 3: Multiply the common prime factors.
The Greatest Common Factor of 9 and 21 is 3.
Find the GCF of 9 and 21 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 21 by 9 21 ÷ 9 = 2 (quotient), The remainder is calculated as 21 − (9×2) = 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 21 is 3.
Finding GCF of 9 and 21 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 apples and 21 oranges. 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 GCF of 9 and 21 GCF of 9 and 21 is 3.
There are 3 equal groups
9 ÷ 3 = 3
21 ÷ 3 = 7
There will be 3 groups, and each group gets 3 apples and 7 oranges.
As the GCF of 9 and 21 is 3, the teacher can make 3 groups.
Now divide 9 and 21 by 3.
Each group gets 3 apples and 7 oranges.
A school has 9 red flags and 21 blue flags. They want to arrange them 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 9 and 21 is 3. So each row will have 3 flags.
There are 9 red and 21 blue flags.
To find the total number of flags in each row, we should find the GCF of 9 and 21.
There will be 3 flags in each row.
A tailor has 9 meters of fabric in one color and 21 meters in another. 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 longest equal length, we have to calculate the GCF of 9 and 21 The GCF of 9 and 21 is 3. The fabric is cut into pieces that are 3 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 9 and 21, which is 3. The length of each piece of the fabric will be 3 meters.
A carpenter has two wooden planks, one 9 cm long and the other 21 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 21 is 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 21 cm, respectively. We have to find the GCF of 9 and 21, 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 63. Find ‘a’.
The value of ‘a’ is 21.
GCF x LCM = product of the numbers
3 × 63 = 9 × a
189 = 9a
a = 189 ÷ 9 = 21
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.