GCF of 21 and 45

GCF of 21 and 45 is the largest possible number that divides 21 and 45 exactly without any remainder. The factors of 21 and 45 are 1, 3, 7, 21 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 21 and 45 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 21 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 21 and 45?

Answer: GCF of 21 and 45 is 3.

Explanation:

The GCF of two non-zero integers, x(21) and y(45), is the greatest positive integer m(3) that divides both x(21) and y(45) without any remainder.

Methods to Find GCF of 21 and 45

Let's look at the different methods for finding the GCF of 21 and 45.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 21 and 45 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 = 45 and Y = 21

GCF(45, 21) = GCF(21, 45 mod 21) = GCF(21, 3)
GCF(21, 3) = GCF(3, 21 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 21 and 45 is 3.

GCF of 21 and 45 by Listing Common Factors

Factors of 21: 1, 3, 7, 21
Factors of 45: 1, 3, 5, 9, 15, 45

There are 2 common factors of 21 and 45, that are 1 and 3. Therefore, the greatest common factor of 21 and 45 is 3.

GCF of 21 and 45 by Long Division

GCF of 21 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 21 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (21) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 21 and 45.

☛ Also Check:

GCF of 21 and 45 Examples

Example 1: For two numbers, GCF = 3 and LCM = 315. If one number is 21, find the other number.

Solution:

Given: GCF (z, 21) = 3 and LCM (z, 21) = 315
∵ GCF × LCM = 21 × (z)
⇒ z = (GCF × LCM)/21
⇒ z = (3 × 315)/21
⇒ z = 45
Therefore, the other number is 45.
Example 2: The product of two numbers is 945. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 945
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 945/3
Therefore, the LCM is 315.
Example 3: Find the GCF of 21 and 45, if their LCM is 315.

Solution:

∵ LCM × GCF = 21 × 45
⇒ GCF(21, 45) = (21 × 45)/315 = 3
Therefore, the greatest common factor of 21 and 45 is 3.

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FAQs on GCF of 21 and 45

What is the GCF of 21 and 45?

The GCF of 21 and 45 is 3. To calculate the GCF of 21 and 45, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 21 and 45, i.e., 3.

How to Find the GCF of 21 and 45 by Long Division Method?

To find the GCF of 21, 45 using long division method, 45 is divided by 21. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 21 and 45?

There are three commonly used methods to find the GCF of 21 and 45.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 21, 45?

The following equation can be used to express the relation between LCM and GCF of 21 and 45, i.e. GCF × LCM = 21 × 45.

How to Find the GCF of 21 and 45 by Prime Factorization?

To find the GCF of 21 and 45, we will find the prime factorization of the given numbers, i.e. 21 = 3 × 7; 45 = 3 × 3 × 5.
⇒ Since 3 is the only common prime factor of 21 and 45. Hence, GCF (21, 45) = 3.
☛ What is a Prime Number?

If the GCF of 45 and 21 is 3, Find its LCM.

GCF(45, 21) × LCM(45, 21) = 45 × 21
Since the GCF of 45 and 21 = 3
⇒ 3 × LCM(45, 21) = 945
Therefore, LCM = 315
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