A day full of math games & activities. Find one near you.

GCF of 9 and 21

GCF of 9 and 21 is the largest possible number that divides 9 and 21 exactly without any remainder. The factors of 9 and 21 are 1, 3, 9 and 1, 3, 7, 21 respectively. There are 3 commonly used methods to find the GCF of 9 and 21 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 9 and 21
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 21?

Answer: GCF of 9 and 21 is 3.

Explanation:

The GCF of two non-zero integers, x(9) and y(21), is the greatest positive integer m(3) that divides both x(9) and y(21) without any remainder.

Methods to Find GCF of 9 and 21

The methods to find the GCF of 9 and 21 are explained below.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 9 and 21 by Long Division

GCF of 9 and 21 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 21 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 9 and 21.

GCF of 9 and 21 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 21 and Y = 9

GCF(21, 9) = GCF(9, 21 mod 9) = GCF(9, 3)
GCF(9, 3) = GCF(3, 9 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 9 and 21 is 3.

GCF of 9 and 21 by Prime Factorization

Prime factorization of 9 and 21 is (3 × 3) and (3 × 7) respectively. As visible, 9 and 21 have only one common prime factor i.e. 3. Hence, the GCF of 9 and 21 is 3.

☛ Also Check:

GCF of 9 and 21 Examples

Example 1: The product of two numbers is 189. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 189
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 189/3
Therefore, the LCM is 63.
Example 2: Find the greatest number that divides 9 and 21 exactly.

Solution:

The greatest number that divides 9 and 21 exactly is their greatest common factor, i.e. GCF of 9 and 21.
⇒ Factors of 9 and 21:
- Factors of 9 = 1, 3, 9
- Factors of 21 = 1, 3, 7, 21
Therefore, the GCF of 9 and 21 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 63. If one number is 21, find the other number.

Solution:

Given: GCF (y, 21) = 3 and LCM (y, 21) = 63
∵ GCF × LCM = 21 × (y)
⇒ y = (GCF × LCM)/21
⇒ y = (3 × 63)/21
⇒ y = 9
Therefore, the other number is 9.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 9 and 21

What is the GCF of 9 and 21?

The GCF of 9 and 21 is 3. To calculate the greatest common factor (GCF) of 9 and 21, we need to factor each number (factors of 9 = 1, 3, 9; factors of 21 = 1, 3, 7, 21) and choose the greatest factor that exactly divides both 9 and 21, i.e., 3.

What is the Relation Between LCM and GCF of 9, 21?

The following equation can be used to express the relation between Least Common Multiple and GCF of 9 and 21, i.e. GCF × LCM = 9 × 21.

How to Find the GCF of 9 and 21 by Prime Factorization?

To find the GCF of 9 and 21, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 21 = 3 × 7.
⇒ Since 3 is the only common prime factor of 9 and 21. Hence, GCF (9, 21) = 3.
☛ What is a Prime Number?

What are the Methods to Find GCF of 9 and 21?

There are three commonly used methods to find the GCF of 9 and 21.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 9 and 21 by Long Division Method?

To find the GCF of 9, 21 using long division method, 21 is divided by 9. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

If the GCF of 21 and 9 is 3, Find its LCM.

GCF(21, 9) × LCM(21, 9) = 21 × 9
Since the GCF of 21 and 9 = 3
⇒ 3 × LCM(21, 9) = 189
Therefore, LCM = 63
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum